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moveto/V matrix currentmatrix A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ +userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N +/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 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200 dict def % the main PSTricks dictionary +tx@Dict begin +/ADict 25 dict def % The arrow dictionaray +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def % return 0 for negative arguments +/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known +/ATAN1 {neg -1 atan 180 sub } def % atan(x) (only one parameter) +/Div { dup 0 eq { pop } { div } ifelse } def % control the division +/tan { dup cos abs 1.e-10 lt + { pop 1.e10 } % return 1.e10 as infinit + { dup sin exch cos div } ifelse % default sin/cos +} def +/Tan { dup sin exch cos Div } def % sin(x)/cos(x) x in degrees +/Acos {dup dup mul neg 1 add dup 0 lt { % arc cos, returns 0 when negative root + pop pop 0 }{ sqrt exch atan} ifelse } def +/NET { neg exch neg exch T } def % change coordinate system to the negative one +/Pyth { dup mul exch dup mul add sqrt } def % Pythagoras, expects 2 parameter +/Pyth2 { % Pythagoras, xA yA xB yB + 3 -1 roll % xA xB yB yA + sub % xA xB yB-yA + 3 1 roll % yB-yA xA xB + sub % yB-yA xA-xB + Pyth } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def % Polar to Cartesian +/Rand { rand 4294967295 div } def % a real random number +%----------------- hv added 20050516 --------------- +/PiDiv2 1.57079632680 def +/Pi 3.14159265359 def +/TwoPi 6.28318530718 def +/Euler 2.71828182846 def +%/e Euler bind def +% +/RadtoDeg { 180 mul Pi div } bind def % convert from radian to degrees +/DegtoRad { Pi mul 180 div } bind def % viceversa +%----------------- hv end--------------------------- +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def +% +/PathLength { + flattenpath /z 0 def + { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } + { /y ED /x ED PathLength@ } + {} + { /y y2 def /x x2 def PathLength@ } + /pathforall load stopped { pop pop pop pop } if + z +} def +% +/STP { .996264 dup scale } def % BP/PT scaling +/STV { SDict begin normalscale end STP } def % +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def + /x x Coef mul def + /y1 y1 Coef mul def + /x1 x1 Coef mul def + x1 0 gt y1 0 gt or x 0 gt or y 0 gt and + { [ y x y1 x1 ] 1 a sub y mul } + { [ 1 0 ] 0 } ifelse + setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { + /b PathLength def + /a ED /z ED /y CLW def + /z y z add def + a 0 gt { + /b b a div def + }{ + a 0 eq { + /b b y sub def + }{ a -3 eq { + /b b y add def } if + } ifelse + } ifelse + [ 0 b b z Div round Div dup 0 le { pop 1 } if ] + a 0 gt { 0 }{ y 2 div a -2 gt { neg }if } ifelse + setdash 1 setlinecap stroke +} def +% +/LineFill { % hv ------------ patch 7 ------------- + gsave + abs /hatchWidthInc ED + abs /hatchSepInc ED + abs CLW add /a ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + 2 setlinecap + systemdict + /setstrokeadjust known { true setstrokeadjust } if + x2 x1 sub 1 add { + x1 a mul y1 moveto 0 y2 rlineto stroke + /x1 x1 1 add + hatchWidthInc 0 gt { CLW add } if + def + hatchSepInc 0 gt hatchWidthInc 0 gt or { + /a a hatchSepInc add def + CLW hatchWidthInc add SLW + } if + } repeat + grestore + pop pop } def +% +/PenroseFill {% on stack: scaling factor + dup dup scale + 1 exch div round /penroseFactor ED + a 0 dtransform round exch round exch + 2 copy idtransform + exch Atan rotate + idtransform pop /a ED + .25 .25 itransform pathbbox + /y2 ED + a Div ceiling cvi /x2 ED /y1 ED + a Div cvi /x1 ED /y2 y2 y1 sub def + clip + newpath + systemdict + /setstrokeadjust known { true setstrokeadjust } if + /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul} + { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall + [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto + i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25 + mul j l + S rmoveto}F i L j L stroke }F}F}F}F + grestore + pop pop +} def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { + ADict begin % hold it local, for end see EndArrow + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict +% +/Arrow { + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /a ED + { 0 h T 1 -1 scale } if + w neg h moveto + 0 0 L w h L w neg a neg rlineto + gsave fill grestore +} def +% +/ArrowD { % the sides are drawn as curves (hv 20071211) + CLW mul add dup + 2 div /w ED + mul dup /h ED + mul /Inset ED + { 0 h T 1 -1 scale } if % changes the direction +% we use y=w/h^2 * x^2 as equation for the control points +% for the coordinates the arrow is seen from top to bottom +% the bottom (tip) is (0;0) + w neg h moveto % lower left of > + w 9 div 4 mul neg h 3 div 2 mul + w 9 div neg h 3 div + 0 0 curveto % tip of > + w 9 div h 3 div + w 9 div 4 mul h 3 div 2 mul + w h curveto % upper left of > + w neg Inset neg rlineto % move to x=0 and inset + gsave fill grestore +} def +% +/Tbar { + CLW mul add /z ED + z -2 div CLW 2 div moveto + z 0 rlineto stroke + 0 CLW moveto +} def +% +/Bracket { + CLW mul add dup CLW sub 2 div + /x ED mul CLW add /y ED /z CLW 2 div def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +% +/Arcto { + /a [ 6 -2 roll ] cvx def + a r + /arcto load stopped { 5 } { 4 } ifelse { pop } repeat + a +} def +% +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +% +/Triangle { + /mtrx CM def + translate + rotate /h ED 2 div /w ED + dup CLW mul /d ED + /h h d w h Atan sin Div sub def + /w w d h w Atan 2 div dup cos exch sin Div mul sub def + mark + 0 d w neg d 0 h w d 0 d + /ArrowA { moveto } def + /ArrowB { } def + false + Line + closepath + mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def + setmatrix pop +} def +% DG/SR modification end +% +/CCA { + /y ED /x ED + 2 copy y sub /dy1 ED + x sub /dx1 ED + /l1 dx1 dy1 Pyth def +} def +% +/CC { + /l0 l1 def + /x1 x dx sub def + /y1 y dy sub def + /dx0 dx1 def + /dy0 dy1 def + CCA + /dx dx0 l1 c exp mul dx1 l0 c exp mul add def + /dy dy0 l1 c exp mul dy1 l0 c exp mul add def + /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def + /x2 x l0 dx mul m mul sub def + /y2 y l0 dy mul m mul sub def + /dx l1 dx mul m mul neg def + /dy l1 dy mul m mul neg def +} def +% +/IC { + /c c 1 add def + c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse + /a a 2 mul 3 div 45 cos b exp div def + CCA + /dx 0 def + /dy 0 def +} def +% +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +% +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +% +/AltCurve { + { false NArray n 2 mul 2 roll + [ n 2 mul 3 sub 1 roll ] aload + /Points ED + n 2 mul -2 roll } + { false NArray } ifelse + n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse +} def +% +/ClosedCurve { + NArray n 3 lt + { n { pop pop } repeat } + { n 3 gt { CheckClosed } if + 6 copy n 2 mul 6 add 6 roll + IC CC x y moveto n { NC } repeat + closepath pop pop + } ifelse +} def +% +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def +% +/FontDot { + DS 2 mul dup + matrix scale matrix concatmatrix exch matrix + rotate matrix concatmatrix exch + findfont exch makefont setfont +} def +% +/Rect { + x1 y1 y2 add 2 div moveto + x1 y2 lineto + x2 y2 lineto + x2 y1 lineto + x1 y1 lineto + closepath +} def +% +/OvalFrame { + x1 x2 eq y1 y2 eq or + { pop pop x1 y1 moveto x2 y2 L } + { y1 y2 sub abs x1 x2 sub abs 2 copy gt + { exch pop } { pop } ifelse + 2 div exch { dup 3 1 roll mul exch } if + 2 copy lt { pop } { exch pop } ifelse + /b ED + x1 y1 y2 add 2 div moveto + x1 y2 x2 y2 b arcto + x2 y2 x2 y1 b arcto + x2 y1 x1 y1 b arcto + x1 y1 x1 y2 b arcto + 16 { pop } repeat + closepath + } ifelse +} def +% +/Frame { + CLW mul /a ED + 3 -1 roll + 2 copy gt { exch } if + a sub /y2 ED + a add /y1 ED + 2 copy gt { exch } if + a sub /x2 ED + a add /x1 ED + 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse +} def +% +/BezierNArray { + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/OpenBezier { + BezierNArray + n 1 eq + { pop pop } + { ArrowA n 4 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + 6 2 roll 4 2 roll ArrowB curveto } ifelse +} def +% +/ClosedBezier { + BezierNArray + n 1 eq + { pop pop } + { moveto n 1 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + closepath } ifelse +} def +% +/BezierShowPoints { + gsave + Points aload length 2 div cvi /n ED + moveto + n 1 sub { lineto } repeat + CLW 2 div SLW [ 4 4 ] 0 setdash stroke + grestore +} def +% +/Parab { + /y0 ED /x0 ED /y1 ED /x1 ED + /dx x0 x1 sub 3 div def + /dy y0 y1 sub 3 div def + x0 dx sub y0 dy add x1 y1 ArrowA + x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB + curveto + /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def +} def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { + /TMatrix [ TMatrix setmatrix ] cvx def + /RAngle [ RAngle pop ] cvx def +} def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +% +/Uput { + /a ED + add 2 div /h ED 2 + div /w ED + /s a sin def + /c a cos def + /b s abs c abs 2 copy gt dup + /q ED + { pop } { exch pop } ifelse def + /w1 c b div w mul def + /h1 s b div h mul def + q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse +} def +% +/UUput { + /z ED + abs /y ED + /x ED + q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse + { x x mul y y mul sub z z mul add sqrt z add } + { q { x s div } { x c div } ifelse abs + } ifelse + a PtoC + h1 add exch + w1 add exch +} def +% +/BeginOL { + dup (all) eq exch TheOL eq or + { IfVisible not { Visible /IfVisible true def } if } + { IfVisible { Invisible /IfVisible false def } if } ifelse +} def +% +/InitOL { + /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def + /Visible { CP OLUnit idtransform T moveto } def + /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def + /BOL { BeginOL } def + /IfVisible true def +} def +% +end +%-----------------------------------------------------------------------------% +% +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ +%% +%% PostScript prologue for PSTricks algorithm parser +%% Version 0.01, 2008/01/01 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%%-----------------------------------------------------------------------------% +% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.02, 2008/04/18 +%% +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +%% Modified by Herbert Voss (hv) - 2008/04/17 +% +10 dict dup begin % hold local + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef + Encoding % replace with given dot names + dup (b) 0 get /Bullet put % get the numerical position of b in ASCII +% % and save /Bullet at this place in Encoding + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put % 67 + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (f) 0 get /Octogon put % 2008-04-18 hv + dup (F) 0 get /BoldOctogon put % 2008-04-18 hv + dup (g) 0 get /SolidOctogon put % 2008-04-18 hv + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put % 65 + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def +CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def + /TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def + /SolidTriangle {TrianglePath fill} def + /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def + /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def + /SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def + /SolidSquare {SquarePath fill} def + /Square {SquarePath .89 .89 scale SquarePath eofill} def + /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def + /PentagonPath { + -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto + 0 574.7 lineto -546.6 177.6 lineto closepath + } def + /SolidPentagon {PentagonPath fill} def + /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def + /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def +%-------------- hv begin 2004/07/25 from: er 2003/03/24 + /HexagonPath { + 0 550 moveto -476 275 lineto -476 -275 lineto + 0 -550 lineto 476 -275 lineto 476 275 lineto closepath + } def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def +% 2008-04-18 hv + /OctogonPath { + 550 dup 22.5 tan mul dup neg dup add /xMove exch def + exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def + /SolidOctogon { OctogonPath fill } def + /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def + /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def +% + /AsteriskPath { + 20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath + } def + /Asterisk { + AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill + } def +% + /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath { + 50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp 60 rotate Basterp + 60 rotate Basterp closepath + } def + /BoldAsterisk {BoldAsteriskPath fill} def + /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def + /CrossPath { + 40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto + -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto + 40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath + } def + /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto + -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto + 80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath + } def + /Add {CrossPath fill} def + /Mul {45 rotate CrossPath fill} def + /BoldAdd {BoldCrossPath fill} def + /BoldMul {45 rotate BoldCrossPath fill} def + /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def + /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def + /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale 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Seyfert]{ + Johannes Albrecht\inst{1}, Marta Calvi\inst{2}, \underline{Marcin Chrzaszcz\inst{3,4}}, \\Laura Gavardi\inst{1}, Jon Harrison\inst{5}, Basem Khanji\inst{2}, George Lafferty\inst{5}, Tatiana Likhomanenko\inst{6}, Eduardo Rodrigues\inst{5}, \\Nicola Serra\inst{3}, Paul Seyfert\inst{7}\\{~}\\ +\textbf{Referees}:\\ Benoit Viaud (Chair) , Matteo Rama, Frederic Machefert (EB) } + \institute[Uni Heidelberg]{ + \inst{1}Dortmund, + \inst{2}Milano Bicocca, + \inst{3}Zurich, \inst{4}IFJ Cracow, \inst{5}Manchester, \inst{6}Yandex, \inst{7}Uni. Heidelberg + } +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + % \begin{frame}\frametitle{Outline} + % \begin{enumerate} + % \item introduction\vspace{.5em} + % \item multivariate technique\vspace{.5em} + % \item normalisation\vspace{.5em} + % % \item backgrounds\vspace{.5em} + % \item expected sensitivity\vspace{.5em} + % \item model dependence\vspace{.5em} data from Reco14Stripping20(r1) + % \end{enumerate} + % Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green} + % \end{frame} + + \begin{frame}\frametitle{Outline} + \tableofcontents + \end{frame} + + + + + \begin{frame} + \frametitle{Yellow pages} + \begin{itemize} + \item TWiki: \href{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}{\url{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}} + \item ANA note: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/v8.pdf}{LHCb-ANA-2014-005} + \item Paper draft: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/paper_v1.pdf}{LHCb-PAPER-2014-X} + \item Target journal: JHEP + \item Conference: Tau 2014 + \end{itemize} + + \end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Introduction} + + \begin{frame} + \frametitle{Status of $\Ptau\to\Pmu\Pmu\Pmu$} + \begin{columns} + \begin{column}{.62\textwidth} + + \includegraphics[width=.95\textwidth]{feymn.png} + + {{ + \begin{itemize} + \item Charged Lepton Flavour Violation process + \item Possible as penguin with neutrino oscillation + \item SM prediction is beyond experimental reach~$O(10^{-40})$ + + \end{itemize} + }} + \end{column} + \begin{column}{.45\textwidth} + \begin{alertblock}{current limits ($ 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{alertblock} + \begin{alertblock}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \item[and many more...] + \end{description} + \end{alertblock} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item Following same approach as other RD searches. + \item Loose stripping selection + \item Multivariate classification in: mass, PID, ``geometry/topology'' + \item Binning optimisation. + \item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$) + \item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$ + \item ``middle sidebands'' for classifier evaluation and tests.($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$). + \item CLs for limit calculation + \end{itemize} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{$\Ptau$ production} + \begin{itemize} + \item Consider five production channels (fractions at $\unit{8}{\TeV}$):\begin{itemize} + \item Prompt $\PDs\to\Ptau$ ($72.4\pm2.7\,\%$) + \item Prompt $\PDplus\to\Ptau$ ($4.2\pm0.7\,\%$) + \item Non-prompt $\PDs\to\Ptau$ ($8.5\pm1.7\,\%$) + \item Non-prompt $\PDplus\to\Ptau$ ($0.17\pm0.04\,\%$) + \item $X_{\Pbottom}\to\Ptau$ (meson or baryon) ($14.7\pm2.3\,\%$) + \end{itemize} + \item Use $\sigma(\Pbottom\APbottom)$ at $\unit{8}{\TeV}$ from LHCb + \item Use Pythia scaling for $\sigma(\Pcharm\APcharm)$ at $\unit{8}{\TeV}$ + \end{itemize} + + \begin{columns} + \column{0.8\textwidth} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$ + \item One can calculate it form: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space + \item \texttt{hep-ex:0604043} + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=1.0\times10^{-3}$ + \end{itemize} + \end{exampleblock} + \column{0.2\textwidth} + {~} + \end{columns} + + \end{frame} + \begin{frame} + \frametitle{Datasets} + \begin{itemize} + \item Data from Reco14Stripping20(r1) + \item Much MC\begin{itemize} + \item 24M Inclusive background events ($\Pbottom\APbottom$ and $\Pcharm\APcharm$) + \item 10M Exclusive background events ($\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$) + \item 2M Signal events (split over 5 production channels) + \item 12M $\PD \to \PK \Ppi \Ppi$ (missID studies) + \item 10M $\PDstar \to \PD(\PK \Pmu \Pnum) \Ppi$ (missID studies) + + \end{itemize} + \item[$\Rightarrow$] Generator level cuts for improved use of computing resources + \begin{itemize} + \item $\sim 14$ times more signal statistics after stripping + \item $\sim 2$ times more background statistics + \end{itemize} + \item Mix $\Ptau$ production on ntuple level instead of reweighting. + \newline$\Rightarrow$ Ease up ntuple usage (no forgotten weighting, no double weighting, \dots) + \end{itemize} + \end{frame} + \section{Selection} + \begin{frame} + \frametitle{Stripping and selection} +{\footnotesize{ +\begin{tabular}{|c|cc|} +\hline + &$\Ptau\to\Pmu\Pmu\Pmu$&$\PDs\to\Pphi\Ppi$\\ +\hline +$\mu^\pm$ , $ \pi^\pm$ &\multicolumn{2}{c|}{} \\ +$p_T$ &\multicolumn{2}{c|}{$>300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +track ghost probability &\multicolumn{2}{c|}{$<0.3 $} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +IP $\chi^2$ &\multicolumn{2}{c|}{$<225 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + + \end{frame} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + \begin{frame} + \frametitle{Triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & $||$ Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{$^1$ triggers in 2012} + \begin{itemize} + \item Cuts changed through 2012 + \item[$\rightarrow$]emulated two different TCKs for 2012 + \item[$\rightarrow$] Found negligible differences + \item Choice of triggers were optimised based on $\dfrac{s}{\sqrt{b}}$ FOM. + \end{itemize} + \end{block}} + % \only<2>{ + % \begin{block}{$^2$ word on Hlt2DiMuonDetached} + % \begin{itemize} + % \item keep it simple here + % \item line unchanged in 2012 + % \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + % \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + % \end{itemize} + % \end{block}} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Multivariate technique} + + \begin{frame} + \frametitle{Geometric likelihood} +Much work has been put in improving our geometric and kinematic classifier: + \begin{itemize} + \item Classify the displaced 3-body decay properties of a signal candidate + \item Revisit variable choice + \item Revisit classification technique + \item More toolkits tried: MatrixNet, NeuroBayes, TMVA + \item Retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ BDT isolation: CERN-THESIS-2013-259) + \item Blending technique. + \end{itemize} + + \end{frame} + + \begin{frame} + \frametitle{Basic Setup - Step I} + \begin{itemize} + \item Train $1/3$ signal MC against $1/2$ background MC + \item variables \begin{itemize} + \item DOCA + \item Vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item Cone isolation + \item BDT isolation + \end{itemize} + \item Using these variables, train several classifiers (''Base'') \\for each of the $\Ptau$ source + \end{itemize} + \end{frame} + + + \begin{frame} + \frametitle{Step II} +\begin{itemize} +\item Train using second $1/3$ signal MC against second $1/2$ background MC. +\item Introduce Blending technique +\end{itemize} + \begin{exampleblock}{Blending technique} + \begin{itemize} + \item For each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, one LD classifier and MatrixNet classifier. + \item One final MatrixNet classifier using the 13 base variables and the base classifiers as input + + \end{itemize} + \end{exampleblock} + \begin{itemize} +\item All evaluation is done on $3rd$ $1/3$ signal sample and middle side-bands. +\item Splitting into independent samples makes the procedure insensitive to +overtraining. +\end{itemize} + + + \end{frame} + + + + \begin{frame} + \frametitle{Performance of Blend classifier} + \begin{itemize} + \item Classifier prefers $\Ptau$ from prompt $\PDs$ + \end{itemize} + \begin{columns} + \begin{column}{.48\textwidth} + \begin{exampleblock}{MC response for different\newline $\Ptau$ production channels} + \includegraphics[width=.95\textwidth]{./mn_sig.png} + \end{exampleblock} + \end{column} + \begin{column}{.48\textwidth} + \begin{exampleblock}{response for $\PDs\to\Pphi\Ppi$\newline data and MC} + \includegraphics[width=.95\textwidth]{./MN_BLEND_FLAT.png} + \end{exampleblock} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Calibration} + \begin{itemize} + \item Assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time) + \item Get correction $\PDs\leadsto\Ptau$ from MC + \item Apply corrections to $\PDs\to\Pphi\Ppi$ on data + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC + % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{MN_BLEND_FLAT.png} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item We used ProbNNmu already in the previous round of the analysis + \item Now use MC12TuneV2 (latest) + \item Two-fold reason:\begin{itemize} + \item Expect better performance than CombDLL variables + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$) + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{PID calibration } + \begin{itemize} + \item Since PIDCalib tool didn't work for us, we choose a phenomenological approach. + \item Many thanks to Barbara Sciascia for help understanding this problem. + \end{itemize} + \begin{exampleblock}{phenomenologic treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$ + \end{itemize} + \end{exampleblock} +\begin{itemize} +\item Many x-checks done. +\item Everything works fine. +\end{itemize} + + \end{frame} + + + + \begin{frame} + \frametitle{Binning optimisation} + \begin{itemize} + \item How to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$ + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier + \item Now: optimise two-dimensions (optimise bin boundaries in both dimensions at the same time) + \item Unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain) + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{Impact of new binning optimisation} + \begin{itemize} + \item Removal of tiny bins which contribute negligible sensitivity + \item Colour: limit obtained, using only this particular bin + \item Number: rank of that bin (1=best sensitivity bin) + \end{itemize} + + ~ + + \begin{columns} + \begin{column}{.5\textwidth} + old analysis + + ~ + + \includegraphics[width=.95\textwidth]{./90CLonebinlimit.pdf} + \end{column} + \begin{column}{.5\textwidth} + new analysis + + (2011 data) + \includegraphics[width=.95\textwidth]{./rank.pdf} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Mass shape} + \begin{itemize} + \item Double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian) + \item Fix fraction to ease calibration:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + Calibrated $\Ptau$ Mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + + + + \section{Normalisation} + + \begin{frame} + \frametitle{Relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012 + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{Normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} (\%) & 8.989 \pm 0.40 & 9.21 \pm 0.35\\ +\hline +\rm{\epsilon_{cal}}^{GEN} (\%) & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} (\%) & 9.927 \pm 0.028 & 9.261 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} (\%) & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\phi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\tau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.89 \pm 0.12 & 1.96 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} (\%) & 35.52 \pm 0.14 \pm 0.14 & 39.3 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} (\%) & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(PDs \to \Pphi \Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\tau}_{D_{s}} & 0.78 \pm 0.04 & 0.80 \pm 0.03 \\ +\hline +\mathcal{B} (\PDs \to \Ptau \Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.898 \pm 0.060 & 0.912 \pm 0.054 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6593 \pm 0.0058 & 0.525 \pm 0.040\\ +\hline +N_{cal} & 28,207 \pm 440 & 52,131 \pm 695\\ +\hline & \\[-0.8em]\hline +\alpha & (3.81 \pm 0.46) \times 10^{-9} & (1.72 \pm 0.23) \times 10^{-9}\\ +\alpha^{trash} & (7.20 \pm 0.98) \times 10^{-9} & (3.37 \pm 0.50) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification} + \begin{itemize} + \item Most dominant: $\PDplus\to\PK\Ppi\Ppi$ + \item Experience from last round: cut away low ProbNNmu range + \item Check remaining data under $\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \item $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$ start to become visible in 2012 + \end{itemize} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{Evil backgrounds} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy + \begin{itemize} + \item Modelled in CONF note + \item Optimised veto in PAPER + \item Right now: both versions in the ANA note + \end{itemize} + \item Baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$ + \begin{itemize} + \item Fits better understood + \item Sensitivity unchanged when removing veto + \item Smaller uncertainty on expected background + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{Remaining backgrounds} + \begin{itemize} + \item Fit exponential to invariant mass spectrum in each likelihood bin + \item Don't use $\pm \unit{30}{\MeV}$ in the fit + \item[$\rightarrow$] Compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier developement} + \end{itemize} + {\begin{center} + Example of most sensitive regions in 2011 and 2012 + \includegraphics[width=0.9\textwidth]{./fits.png} + + \end{center}} + \end{frame} + + \section{Expected limit} + + \begin{frame} + \frametitle{expected limit} + \begin{itemize} + \item Consider nuisance parameters from background fit, signal pdf calibration, normalisation + \item Nuisance parameters due to $\Ptau$ production, normalization. + \item Limit for combined 2011+2012 analysis + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{Sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.0 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{./banana.png} + \end{frame} + + + + \section{Model dependence} + + \begin{frame} + \frametitle{Model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not applicable to New Physics with small $m_{\APmuon\Pmuon}$ + \item Model description in \texttt{arXiv:0707.0988} + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms + \end{itemize} + \only<2->{ + \begin{itemize} + \item With radiative distribution limit gets worse by $51\,\%$ (dominantly from the $\Peta$ veto) + \item The other four Dalitz distributions behave nicely (within $7\,\%$) + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.pdf} + \includegraphics[width=.331\textwidth]{./gammallrr.pdf} + \includegraphics[width=.331\textwidth]{./gammarad.pdf} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.pdf} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.pdf} +} + + \end{frame} + + + % \begin{frame} + % \frametitle{Conclusion} + % \begin{columns} + % \begin{column}{.55\textwidth} + % \begin{itemize} + % \item finally all pieces put together + % \item model (in)dependence of $\Peta$ veto investigated + % \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + % \end{itemize} + % \end{column} + % \begin{column}{.45\textwidth} + % \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + % \end{column} + % \end{columns} + + % \end{frame} + + + \section{Unblinded results} + + \begin{frame} + \frametitle{Unblinding 1} +\begin{columns} +\column{1in}{~} +\column{3in} +'' +THERE came a day at summer’s full \\ +Entirely for us \\ +I thought that such were for the saints, \\ +Where revelations be. ''\footnote{E.Dickinson} \\ + \column{1in}{~} +\end{columns} +{~}\\ +{~}\\ +\begin{Large} +On Monday $4^{th}$ of August we were given the permission to unblind. +\end{Large} + + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 2} +\begin{itemize} +\item Unfortunately no big ''revelations'' were there: +\item 2011 numbers: +\end{itemize} + \includegraphics[width=1.\textwidth]{2011.png} + + \end{frame} + + \begin{frame} + \frametitle{Unblinding 3} +\begin{itemize} +\item Unfortunately no big ''revelations'' were also in 2012 data: + +\end{itemize} + \includegraphics[width=1.1\textwidth]{2012.png} + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 4} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + \begin{frame} + \frametitle{Conclusions} + \begin{columns} + \column{2.5in} + \begin{itemize} + \item We didn't find NP (yet). + \item Limits set with full LHCb dataset. + \item Awaiting for the future data! + \end{itemize} +\column{2.5in} + + \includegraphics[width=1\textwidth]{TauLFV_UL_2013001.pdf} + + + + \end{columns} + \begin{itemize} + \item We would like to thank our referees for very friendly,thorough and fruitful review. + \item With this presentation we ask collaboration for approval. + \end{itemize} + + + \end{frame} + + + +\end{document} diff --git a/FCC_LFV/mchrzasz2.aux b/FCC_LFV/mchrzasz2.aux new file mode 100644 index 0000000..72b4ca1 --- /dev/null +++ b/FCC_LFV/mchrzasz2.aux @@ -0,0 +1,132 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global \let \oldnewlabel\newlabel +\gdef 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[2][]{Outline0.7}{Backgrounds}{} +\BOOKMARK [2][]{Outline0.8}{Model dependence}{} +\BOOKMARK [2][]{Outline0.9}{Results}{} +\BOOKMARK [2][]{Outline0.10}{Future of LFV at hadron colliders}{} diff --git a/FCC_LFV/mchrzasz2.pdf b/FCC_LFV/mchrzasz2.pdf new file mode 100644 index 0000000..1587b92 --- /dev/null +++ b/FCC_LFV/mchrzasz2.pdf Binary files differ diff --git a/FCC_LFV/mchrzasz2.snm b/FCC_LFV/mchrzasz2.snm new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/FCC_LFV/mchrzasz2.snm diff --git a/FCC_LFV/mchrzasz2.synctex.gz b/FCC_LFV/mchrzasz2.synctex.gz new file mode 100644 index 0000000..a669bf8 --- /dev/null +++ b/FCC_LFV/mchrzasz2.synctex.gz Binary files differ diff --git a/FCC_LFV/mchrzasz2.tex b/FCC_LFV/mchrzasz2.tex new file mode 100644 index 0000000..efc9e42 --- /dev/null +++ b/FCC_LFV/mchrzasz2.tex @@ -0,0 +1,921 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} +\usepackage{feynmp} +\usepackage{pst-pdf} +\usepackage{hyperref} +\usepackage{xcolor} +\def\BF {{\ensuremath{\cal B}\xspace}} + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} +\title[Lepton Flavour Violation at $\color{white}\tau$ decays]{Lepton Flavour Violation at $\color{white}\tau$ decays} +\author{Marcin Chrz\k{a}szcz$^{1,2}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow \\{~}\\ FCC WG on experiments with the CERN injectors } +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + % \begin{frame}\frametitle{Outline} + % \begin{enumerate} + % \item introduction\vspace{.5em} + % \item multivariate technique\vspace{.5em} + % \item normalisation\vspace{.5em} + % % \item backgrounds\vspace{.5em} + % \item expected sensitivity\vspace{.5em} + % \item model dependence\vspace{.5em} data from Reco14Stripping20(r1) + % \end{enumerate} + % Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green} + % \end{frame} + + \begin{frame}\frametitle{Outline} + \tableofcontents + \end{frame} +\section{Lepton Flavour Violation status} +\begin{frame}\frametitle{Lepton Flavour/Number Violation} +\begin{small} + Lepton Flavour Violation(LFV): +\end{small} + + +\begin{footnotesize} + +After $\Pmuon$ was discovered (1936) it was natural to think of it as an excited $\Pelectron$. +\begin{columns} +\column{3in} +\begin{itemize} +\item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$ +\item Unless another $\Pnu$, in intermediate vector boson loop, cancels. +\end{itemize} + +\column{2in} +{~}\includegraphics[width=0.98\textwidth]{rabi.png} + +\end{columns} +\begin{columns} +\column{0.5in} +{~} +\column{3in} +\begin{block}{I.I.Rabi:} +"Who ordered that?" +\end{block} +\column{0.3in}{~} +\column{2in} +{~}\includegraphics[scale=0.08]{II_Rabi.jpg} + +\end{columns} + + +\begin{itemize} +\item Up to this day charged LFV is being searched for in various decay modes. +\item LFV was already found in neutrino sector (oscillations). +\end{itemize} +\end{footnotesize} + + +\begin{footnotesize} + +\begin{columns} +\column{3.5in} +\begin{small} + Lepton Number Violation (LNV) +\end{small} + +\begin{itemize} +\item Even with LFV, lepton number can be a conserved quantity. +\item Many NP models predict it violation (Majorana neutrinos) +\item Searched in so called Neutrinoless double $\beta$ decays. +\end{itemize} + +\column{1.5in} +\includegraphics[width=0.73\textwidth]{Double_beta_decay_feynman.png} + +\end{columns} + +\end{footnotesize} +%Double_beta_decay_feynman.png + + % \textref{M.Chrz\k{a}szcz 2014} +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{LFV at B-factories} +\begin{frame}\frametitle{LFV at B-factories} +\begin{columns} +\column{0.2in} +{~} +\column{2.5in} +$\sigma(\Pelectron \APelectron \to \Ptau^+ \Ptau^-)=0.919~\nanobarn$ +\begin{itemize} +\item Clean environment. +\end{itemize} +\includegraphics[width=0.73\textwidth]{upsilon4s.png} +\begin{itemize} +\item High efficiency: $5-10\%$ +\item Background free. +\item Efficient and simple tag. +\end{itemize} + +\column{2.5in} +Signal extraction: +$M_{\mu\gamma}=\sqrt{(E^{CM}_{sig})^2 - (p_{sig}^{CM})^2}$ +$\Delta E = E_{sig}^{CM}-E_{beam}^{CM}$ +$H_l = \sum_{ij} \dfrac{|\overrightarrow{p_j}||\overrightarrow{p_i}| P_l(\cos \Omega_{ij}) }{s}$ +\includegraphics[width=0.73\textwidth]{dedm.png} + + +\end{columns} + + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\section{LHCb detector} + +\begin{frame}\frametitle{Hadron collider - LHCb} +\begin{columns} +\column{3.in} +\begin{center} +\includegraphics[width=0.98\textwidth]{det.jpg} +\end{center} + +\column{2.0in} +\begin{footnotesize} + + + LHCb is a forward spectrometer: + \begin{itemize} + \item Excellent vertex resolution. + \item Efficient trigger. + \item High acceptance for $\Ptau$ and $\PB$. + \item Great Particle ID + \end{itemize} + + + +\end{footnotesize} +\end{columns} + +\end{frame} + + +\begin{frame}\frametitle{Analysis approach} +\begin{columns} +\column{0.2in} +{~} +\column{2.5in} +B factories + + +\column{2.5in} +LHCb, ($7-8 TeV$, 2011-2012 data) + +\end{columns} +\begin{columns} +\column{2.5in} + + +\begin{enumerate} + \item Clean signal: $\APelectron\Pelectron\to\APtauon\Ptauon$ + \item Calculate the thrust axis + \item "Partial tag" of the other $\tau$ + \item Small cross section $0.919nb$ +\end{enumerate} + +\column{2.5in} + +\begin{enumerate} +\item Inclusive $\tau$ cross section: \newline $\sim80{\micro\barn}$. + \item $~\sim 10^{11} \tau$ produced. + \item Dominant contribution: \newline $\PDs\to\Ptau\Pnut$ ($78\%$) + \item No tag possible. +\end{enumerate} + + +\end{columns} +\end{frame} + + \begin{frame} + \section{Selection} + \frametitle{Strategy} + \begin{itemize} + \item Blind analysis. + \item Loose selection. + \item Multivariate classification in: mass, PID($\mathcal{M}_{PID}$), geometry($\mathcal{M}_{3body}$). + \item Binning optimisation. + \item Consider 2012($8~\TeV$) and 2011($7~\TeV$) data separately. + \item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$). + \item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$. + \item ``middle sidebands'' for classifier evaluation and tests: ($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$). + \item CLs for limit calculation. + \end{itemize} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{$\color{white} \tau$ production} + \begin{itemize} + \item $\Ptau$'s in LHCb come from five main sources: + \end{itemize} + \begin{center} + + +\begin{tabular}{| c | c | c | } +\hline + Mode & $7~\TeV$ & $8~\TeV$ \\ \hline + Prompt $\PDs\to\Ptau$ & $71.1\pm3.0\,\%$ & $72.4\pm2.7\,\%$ \\ + Prompt $\PDplus\to\Ptau$ & $4.1\pm0.8\,\%$ & $4.2\pm0.7\,\%$ \\ + Non-prompt $\PDs\to\Ptau$ & $9.0\pm2.0\,\%$ & $8.5\pm1.7\,\%$ \\ + Non-prompt $\PDplus\to\Ptau$ & $0.18\pm0.04\,\%$ & $0.17\pm0.04\,\%$ \\ + $X_{\Pbottom}\to\Ptau$ & $15.5\pm2.7\,\%$ & $14.7\pm2.3\,\%$ \\ \hline + +\end{tabular} + \end{center} + + + \begin{columns} + \column{0.8\textwidth} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$. + \item One can calculate it from: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space. + \item \texttt{hep-ex:0604043}. + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=(1.0\pm0.1) \times10^{-3}$. + \end{itemize} + \end{exampleblock} + \column{0.2\textwidth} + {~} + \end{columns} + + \end{frame} + + \begin{frame} + \frametitle{Triggers at LHCb} +\begin{itemize} +\item LHCb uses complex trigger\footnote{\href{http://arxiv.org/abs/1211.3055}{\color{blue}arxiv 1211.3055}} +\item $\mathcal{O}(100)$ trigger lines. +\item Lines change with data taking. +\item Optimized choice of triggers based on $\dfrac{s}{\sqrt{b}}$ FOM. +\item Evaluated different triggers used in 2012 data taking. +\item Found negligible differences in trigger efficiencies. +\end{itemize} + + + + + \end{frame} + + \section{Multivariate technique} + + \begin{frame} + \frametitle{Geometric likelihood} + + \begin{itemize} + \item As mentioned in LHC we have different production sources of $\Ptau$'s. + \item Each source has different detector response signature. + \item To maximise our performance we trained classifiers for each of the $\Ptau$ sources using: + \begin{itemize} + \item Kinematic properties of $\Ptau$ candidate. + \item Geometric properties of $\Ptau$ candidate, like pointing angle, DOCA, Vertex $\chi^2$, flight distance. + \item Isolations, for vertex and individual tracks. + \end{itemize} + \item After training the individual classifiers one that combines all this information in a single classifier on mixed sample of $\Ptau$'s. + \item This technique is known as Blending or Ensemble learning. + \item Using this approach we gain $6\%$ sensitivity! + \end{itemize} + + + \end{frame} + + \begin{frame} + \frametitle{Performance of Blend classifier} + \begin{itemize} + \item Classifier prefers $\Ptau$'s from prompt $\PDs$, the dominant channel. + \end{itemize} + \begin{columns} + \begin{column}{.49\textwidth} + \begin{exampleblock}{MC response for different\newline $\color{white} \tau$ production channels} + \includegraphics[width=.98\textwidth]{./mixing.pdf} + \end{exampleblock} + \end{column} + \begin{column}{.49\textwidth} + \begin{exampleblock}{Response for $\color{white} D_s \rightarrow \phi\pi$\newline data and MC} + \includegraphics[width=.98\textwidth]{./dataMC.pdf} + \end{exampleblock} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Calibration} + \begin{itemize} + \item Assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time), which is correct in MC. + \item Get correction $\PDs\leadsto\Ptau$ from MC. + \item Apply corrections to $\PDs\to\Pphi\Ppi$ on data. + \end{itemize} + + \begin{columns} + + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{m3body_2012.pdf} + \end{column} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC. + % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +% PID + + \begin{frame} + \frametitle{PID} +\begin{itemize} +\item Classifier trained on inclusive MC sample. +\item Using information from: RICH, Calorimeters, Muon system and tracking. +\item Correct for the MC efficiency using control channel: $\PDs \to \Pphi(\Pmu\Pmu) \Ppi$ and $\PB \to \PJpsi(\Pmu\Pmu) \PK$ +\end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{mPID_2012.pdf} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 + \begin{frame} + \frametitle{Binning optimisation} + \begin{itemize} + \item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane. + \item In 2D we group the events in groups(bins) + \item Bins are optimised using $CL_s$ method. + \item The lowest bins are rejected, because they do not contribute to the limit sensitivity. + \item In the remaining bins a fit to mass side-bands is performed in order to estimate number of expected background in signal window. + \end{itemize} +\begin{columns} +\column{2.5in} +\center{2011}\\ + \includegraphics[width=.85\textwidth]{2D_2011.pdf} +\column{2.5in} +\center{2012}\\ + \includegraphics[width=.85\textwidth]{2D_2012.pdf} + + +\end{columns} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Mass shape} + \begin{itemize} + \item Double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian). + \item Fix fraction to ease calibration. + \item Correct mass by MC:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + Calibrated $\Ptau$ Mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + + + + \section{Normalisation} + + \begin{frame} + \frametitle{Relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection efficiency. + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$. + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012. + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification} + \begin{columns} + \column{3in} + \begin{itemize} + \item Dominant: $\PDplus\to\PK\Ppi\Ppi$. + \item Also seen $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$. + \item All contained in the lowest $\mathcal{M}_{PID}$ bin. + % \item Experience from last round: cut away \\low ProbNNmu range + % \item Check remaining data under \\$\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + % \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \end{itemize} + \column{2in} + \includegraphics[width=.95\textwidth]{./WMH.pdf} + \end{columns} + \includegraphics[width=.45\textwidth]{./trash.pdf}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~} + \includegraphics[width=.45\textwidth]{./mPID_2012.pdf} + \end{frame} + + + \begin{frame} + \frametitle{Dangerous backgrounds} + \begin{columns} + \column{3in} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass. + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy: + \begin{itemize} + \item Model it + \item \underline{Remove it} with dimuon mass cut: + \begin{itemize} + + + \item Fits better understood. + \item Sensitivity unchanged when removing veto. + \item Smaller uncertainty on expected background. + \end{itemize} + \end{itemize} + \end{itemize} + \column{2in} + \includegraphics[width=.95\textwidth]{./etaMass.pdf}\\ + \includegraphics[width=.95\textwidth]{./etaDalitz.pdf} + + \end{columns} + + \end{frame} + + \begin{frame} + \frametitle{Remaining backgrounds} + \begin{itemize} + \item Fit exponential to invariant mass spectrum in each likelihood bin. + \item Don't use blinded region ( $\pm \unit{30}{\MeV}$ ). + \item[$\rightarrow$] Compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier development} + \end{itemize} + {\begin{center} + Example of most sensitive regions in 2011 and 2012 + \includegraphics[width=0.9\textwidth]{./fits.png} + + \end{center}} + \end{frame} + + + + \section{Model dependence} + + \begin{frame} + \frametitle{Model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not constraining to New Physics with small $m_{\APmuon\Pmuon}$. + \item Model description in \href{http://arxiv.org/abs/0707.0988}{\color{blue}\texttt{arXiv:0707.0988}} by S.Turczyk. + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms. + \end{itemize} + \only<2->{ + \begin{itemize} + \item With radiative distribution limit gets worse by a factor of $1.5$ (dominantly from the $\Peta$ veto). + \item The other four Dalitz distributions behave nicely (within $7\,\%$). + \end{itemize} + \begin{center} + \includegraphics[width=.5\textwidth]{./sigDalitz.pdf} + \end{center} + + + } + \only<1>{ +\begin{columns} + \column{0.33\textwidth} + \includegraphics[width=.95\textwidth]{./gammallll2.pdf}\\ + \includegraphics[width=.95\textwidth]{./gammarad-llll2.pdf} + + + \column{0.33\textwidth} + \includegraphics[width=.95\textwidth]{./gammallrr2.pdf}\\ + \includegraphics[width=.95\textwidth]{./gammarad-llrr2.pdf} + + \column{0.33\textwidth} + \includegraphics[width=.95\textwidth]{./gammarad2.pdf}\\ + +% \begin{itemize} +% \item Same models as in Z.Was \href{https://indico.cern.ch/event/300387/session/7/contribution/33}{\color{blue}talk} +% \end{itemize} +{~}\\ {~}\\ {~}\\ {~}\\ {~}\\ + + \end{columns} +} + + \end{frame} + + + % \begin{frame} + % \frametitle{Conclusion} + % \begin{columns} + % \begin{column}{.55\textwidth} + % \begin{itemize} + % \item finally all pieces put together + % \item model (in)dependence of $\Peta$ veto investigated + % \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + % \end{itemize} + % \end{column} + % \begin{column}{.45\textwidth} + % \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + % \end{column} + % \end{columns} + + % \end{frame} + + + \section{Results} + + \begin{frame} + \frametitle{Results} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$\color{red}4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$\color{pink}5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + \begin{frame} + \frametitle{"The Rule of Three"} + \begin{columns} + % \column{2.5in} + \begin{column}{2.1in} + \begin{alertblock}{ $\Ptau \to \Pmu \Pmu \Pmu$ limits ($ \color{white} 90\,\%$ CL)} + + \begin{description} + \item[BaBar(FC)] $3.3\times 10^{-8}$ + \item[Belle(FC)] $2.1\times 10^{-8}$ + \item[LHCb(CLs)] $4.6\times 10^{-8}$ + \item[HFAG(CLs)] $1.2 \times 10^{-8}$ + \end{description} + \end{alertblock} +\end{column} + \begin{column}{2.5in} + \includegraphics[width=1\textwidth]{zom.png}\\ + {~}From A.Lusiani \href{https://indico.cern.ch/event/300387/session/6/contribution/12}{\color{blue}talk} + +\end{column} + + \end{columns} + {~}\\ + To conclude: + \begin{itemize} + \item LHCb updated $\Ptau \to \Pmu \Pmu \Pmu$ with full data set. + \item We are getting close to B-factories. + \item Thanks to 3 experiments we have a world limit: $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL. + \end{itemize} + + + \end{frame} + \begin{frame} + %\frametitle{More nasty background} +\begin{center} +\begin{Huge} + +Future of $\Ptau \to 3\Pmu$ at hadron colliders. +\end{Huge} +\end{center} + + + + \end{frame} + + + + + +\section{Future of LFV at hadron colliders} + \begin{frame} + \frametitle{More nasty background} +\includegraphics[width=1\textwidth]{b1.png}\\ + + \end{frame} + + \begin{frame} + \frametitle{More nasty background} +\includegraphics[width=1\textwidth]{b2.png}\\ + + \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{LFV at SHIP experiment} +\begin{columns} +\column{2.5in} +\begin{center} +\includegraphics[width=0.2\textwidth]{SHIP-Full_Black_146x195.png} + +\end{center} +\begin{itemize} +\item Beam dump experiment from SPS. +\item Designed to study long living particles e.g.. HNL. +\item Main interest are particles coming from charm decays. +\item Charm decays are also an excellent source of $\Ptau$ decays:\\ +$Br(\PDsplus \to \APtauon \Pnut )= (5.6 \pm 0.4 )\%$ +\\{~}\\{~}\\{~}\\{~}\\ + + +\end{itemize} + +\column{2.5in} + +%\begin{center} +\includegraphics[width=0.98\textwidth]{setup-sketch.pdf}\\ +\includegraphics[width=0.98\textwidth]{ship.png}\\ +{~}{~}{~}{~} +\\{~}\\{~}\\{~}\\{~}\\ +%\end{center} +\end{columns} + + \end{frame} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} +\frametitle{LFV at SHIP experiment: Idea 1} +\begin{columns} +\column{2.5in} +\begin{itemize} +\item Put a specific $\Ptau \to 3 \Pmu$ detector just after the target. +\item Huge number of $\Ptau$ produced: $1.2 \times 10^{15}$! +\item The numbers are very encouraging! +\item What is the mass resolution? +\end{itemize} +%\includegraphics[width=0.65\textwidth]{tungsten.png}\\ +\column{2.5in} +{~}\\ +Based on SHIP $\Ptau \to 3\Pmu$ WG:\\ +\begin{small} +L.Shchutska, G.Mitselmakher, J.Harrison, C.Parkes, N.Serra, E. Rodrigues, B.Storaci, A.Golutvin ,M.Chrz\k{a}szcz\\\end{small} +\includegraphics[width=0.98\textwidth]{setup-sketch1.png}\\ +%{~}\\{~}\\{~}\\{~}\\{~}\\{~}\\{~}\\{~}\\ +%\includegraphics[width=0.7\textwidth]{carbon.png}\\ +\end{columns} + +\begin{columns} +\column{0.1in} +{~}\\ +\column{1.7in} +\includegraphics[width=0.95\textwidth]{tungsten.png}\\ +\column{1.7in} +\includegraphics[width=0.95\textwidth]{carbon.png}\\ +\column{1.5in} +{~}\\ +\end{columns} + + + \end{frame} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} +\frametitle{Momentum correction} +\includegraphics[width=0.95\textwidth]{corrections.png}\\ +\begin{itemize} +\item With correction of momentum after the target the resolution is better. +\item However still not good enough to perform this measurement. +\item Conclusions: momentum of the muons needs to be measured before absorber and on thin target. +\end{itemize} + \end{frame} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} +\frametitle{LFV at SHIP experiment: Idea 2} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{ship2.png}\\ +\includegraphics[width=0.95\textwidth]{det.png}\\ +\column{2.5in} +\begin{itemize} +\item Multiple scattering is negligible. +\item $\Ptau$ vertex outside the target. +\item Reduce $\Ptau$ flux by a factor of $100$. +\item First estimate of sensor \\ +radius :$\sim 2.5~\mm$ +\item Evaluated acceptance: $33\%$ +\item Work ongoing. +\end{itemize} + + +\end{columns} + + \end{frame} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} +\frametitle{LFV at injectors for FCC} +\begin{itemize} +\item First thought: Detector similar to LHCb. +\item Lets try to make ,,zero approximation'' using LHCb analysis. +\item Ingredients: +\begin{itemize} +\item Acceptance:$\sim10~\%$. +\item Pre-Selection and tracking:$\sim10~\%$. +\item Trigger:$\sim40~\%$. +\item Selection(trash bins):$\sim50~\%$. +\item In total: $0.2~\%$. +\end{itemize} +\item Not bad so far! +\end{itemize} + + \begin{exampleblock}{Observation:} +The total efficiency can be increased by factor $2-5$ if detector is optimised for $\Ptau$'s. + \end{exampleblock} + + + +\end{frame} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame} +\frametitle{LFV at injectors for FCC - Pileup} + +\begin{columns} +\column{3in} +\includegraphics[width=0.95\textwidth]{multvsgeo.pdf} +\column{2in} +\begin{itemize} +\item Not clear correlation with multiplicity. +\item Good for pile-up increase. +\end{itemize} + +\end{columns} + + + \begin{exampleblock}{Observation:} + Pile up in LHCb regime is not a problem. + \end{exampleblock} + +\end{frame} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\begin{frame} +\frametitle{LFV at injectors for FCC - Idea to shoot at} +\begin{columns} +\column{2.5in} +\begin{itemize} +\item Let's assume that FCC will be a $\Pelectron \APelectron$ collider.\\ LHC tunnel - $\Pelectron \APelectron$ booster. +\item We would collect $10^{12-13}~\PZ$ decays. +\item $Br(\PZ \to \Ptauon \APtauon) = 3.370 \pm0.008\%$. +\item Number of $\Ptau$: $6.7\times 10^{10-11}$. +\only<2> +{ +\item Belle2: $50 \invab \times 2 \times 0.919 \nanobarn = 9.2 \times 10^{10}~\tau$'s + +} + +\end{itemize} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{lumi.png} + + +\end{columns} + +\only<2> +{ +\begin{columns} +\column{0.3in} +{~} +\column{2.5in} +\begin{alertblock}{Reminder:} +\begin{itemize} +\item $\epsilon_{\Ptau\to 3\mu}^{BaBar}= 6.6\pm0.6\%$ +\item $\epsilon_{\Ptau\to 3\mu}^{Belle}= 7.6\pm0.6\%$ +\item $\epsilon_{\Ptau}^{ALEPH}= \sim 50\%$ + +\end{itemize} +\end{alertblock} + + \column{2.5in} +\begin{itemize} +\item There is a factor of $8$ to gain \\ just in efficiency! + +\end{itemize} + \end{columns} + +} +\only<3> +{ +\begin{columns} +\column{0.3in} +{~} +\column{2.5in} + \includegraphics[width=0.95\textwidth]{emumu1.png} + \column{2.0in} +\begin{exampleblock}{Reminder 2:} +\begin{itemize} +\item \small{In $\Pelectron \APelectron$ machines in contrast to hadron colliders the limit doesn't necessary follow $\sqrt{\mathcal{L}}$}. +\item Another factor to gain. + + + +\end{itemize} +\end{exampleblock} + \end{columns} + +} + + + + +\end{frame} + + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Beyond LFV} + +\begin{columns} +\column{0.2in} +{~} +\column{3in} +$\Ptau$'s at hadron collider have limit use! +At $\Pelectron \APelectron$ we get for free: +\begin{itemize} +\item All LFV(at hadron colliders most decays are not possible). +\item $V_{us}$ from $\Ptau$. +\item Lepton universality tests\\(anomally from LEP):\\ \begin{footnotesize}$\dfrac{2BR(\PW\to \Ptau \Pnut)}{BR(\PW\to \Pmu \Pnum)+ BR(\PW\to e \Pnue)}$=1.077(0.026). \end{footnotesize} +\item Hadronic spectral functions. +\item etc. +\end{itemize} +\column{2.0in} + \includegraphics[width=0.95\textwidth]{Vus.png} +\end{columns} +\end{frame} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame} +\frametitle{Conclusions} + +\begin{itemize} +\item LFV is possible at hadron machines! +\item LHCb already caught up with B-factories. +\item In future there are many different possibilities for $\Ptau$ factories. +\item Many studies ongoing. + +\end{itemize} + + + +\end{frame} + + + + + + +\end{document} diff --git a/FCC_LFV/mchrzasz2.toc b/FCC_LFV/mchrzasz2.toc new file mode 100644 index 0000000..4c28369 --- /dev/null +++ b/FCC_LFV/mchrzasz2.toc @@ -0,0 +1,12 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} +\beamer@sectionintoc {1}{Lepton Flavour Violation status}{3}{0}{1} +\beamer@sectionintoc {2}{LFV at B-factories}{4}{0}{2} +\beamer@sectionintoc {3}{LHCb detector}{5}{0}{3} +\beamer@sectionintoc {4}{Selection}{7}{0}{4} +\beamer@sectionintoc {5}{Multivariate technique}{10}{0}{5} +\beamer@sectionintoc {6}{Normalisation}{16}{0}{6} +\beamer@sectionintoc {7}{Backgrounds}{17}{0}{7} +\beamer@sectionintoc {8}{Model dependence}{20}{0}{8} 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Seyfert\inst{7}}} + + \institute[Uni Heidelberg]{ + \inst{1}Dortmund, + \inst{2}Milano Bicocca, + \inst{3}Cracow, \inst{4}Zurich, \inst{5}Manchester, \inst{6}Yandex, \inst{7}Heidelberg University + } + + \date{\today} + \subject{} + + + \AtBeginSection[] + { + \begin{frame}{} + \tableofcontents[currentsection,currentsubsection] + \end{frame} + } + + + \begin{document} + \begin{frame} + \titlepage + \end{frame} + + + \begin{frame} + \begin{enumerate} + \item introduction\vspace{.5em} + \item multivariate technique\vspace{.5em} + \item choice of triggers\vspace{.5em} + \item normalisation\vspace{.5em} + \item backgrounds\vspace{.5em} + \item expected sensitivity\vspace{.5em} + \item model dependence\vspace{.5em} + \end{enumerate} + Major news wrt.\ the previous analysis rounds highlighted in \textcolor{darkgreen}{green} + \end{frame} + + \section{introduction} + + \begin{frame} + \frametitle{Status $\Ptau\to\Pmu\Pmu\Pmu$} + \begin{columns} + \begin{column}{.62\textwidth} + \begin{fmffile}{sm} + \begin{fmfgraph*}(200,150) + \fmfstraight + \fmfleft{is3,is2,is1,i1,i2,i3,i4,i5,i6} + \fmfright{os3,os2,os1,o1,o2,o3,o4,o5,o6} + + + \fmf{phantom}{o1,g1} + \fmf{phantom,tension=1.5}{g1,i1} + + \fmffreeze + + \fmf{photon, tension=2.,lab.side=left, lab=$\Pphoton$}{g1,g2} + \fmf{fermion,lab.side=left,label=$\APmuon$}{o3,g2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g2,o5} + \fmf{phantom,tension=1.5}{i6,g2} + + \fmffreeze + + + \fmf{fermion,lab.side=left,label=$\Pgtm$}{i1,w1} + \fmf{dashes,lab.side=right,label=$\PWminus$}{w1,w2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{w2,o1} + + + \fmfipath{p[]} + \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} + \fmffreeze + \fmfiset{p1}{vpath1(__w1,__w2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + \end{fmfgraph*} + + \end{fmffile} + {\footnotesize{ + \begin{itemize} + \item charged Lepton Flavour Violation process + \item possible as penguin with neutrino oscillation + \item unmeasurable small + \end{itemize} + }} + \end{column} + \begin{column}{.37\textwidth} + \begin{block}{current limits ($ 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{block} + \begin{block}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \end{description} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{$\Ptau$ production} + \begin{itemize} + \item consider five production channels (fractions at $\unit{8}{\TeV}$):\begin{itemize} + \item prompt $\PDs\to\Ptau$ ($73.1\pm3.9\,\%$) + \item prompt $\PDplus\to\Ptau$ ($0.42\pm0.43\,\%$) + \item non-prompt $\PDs\to\Ptau$ ($9.7\pm2.1\,\%$) + \item non-prompt $\PDplus\to\Ptau$ ($0.02\pm0.02\,\%$) + \item $X_{\Pbottom}\to\Ptau$ (meson or baryon) ($16.8\pm3.0\,\%$) + \end{itemize} + \item \textcolor{darkgreen}{use $\sigma(\Pbottom\APbottom)$ at $\unit{8}{\TeV}$ from LHCb} + \item \textcolor{darkgreen}{use Pythia scaling for $\sigma(\Pcharm\APcharm)$ at $\unit{8}{\TeV}$} + \end{itemize} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item old analysis: used upper limit + \item now: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space + \item \texttt{hep-ex:0604043} + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=1\pm1\times10^{-4}$ + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item mostly as in many rare decay searches: + \item loose stripping selection + \item multivariate classification in: mass, PID, ``geometry/topology'' + \item relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$) + \item invariant mass fit for expected background in each likelihood bin\newline fit in $m-m_{\Ptau}>\unit{30}{\MeV}$ + \item ``middle sidebands'' for classifier evaluation ($\unit{20}{\MeV}300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +\textcolor{darkgreen}{track ghost probability} &\multicolumn{2}{c|}{\textcolor{darkgreen}{$<0.3 $}} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +\textcolor{darkgreen}{IP $\chi^2$} &\multicolumn{2}{c|}{$<225^1 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + +{\footnotesize{$^1$ different LoKi functor}} + \end{frame} + + \section{multivariate technique} + + \begin{frame} + \frametitle{``geometric likelihood''} + \begin{itemize} + \item classify the displaced 3-body decay properties of a signal candidate + \item revisit variable choice + \item revisit classification technique + \item \textcolor{darkgreen}{more toolkits tried: MatrixNet, NeuroBayes}, TMVA + \item \textcolor{darkgreen}{retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ Laura's BDT isolation: CERN-THESIS-2013-259)} + \end{itemize} + + \end{frame} + \begin{frame} + \frametitle{setup} + \begin{itemize} + \item train $1/3$ signal MC against $1/2$ background MC + \item variables \begin{itemize} + \item $3\times$ DOCA + \item vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item cone isolation + \item \textcolor{darkgreen}{BDT isolation} + \end{itemize} + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{futher tweaking} + \begin{itemize} + \item \textcolor{darkgreen}{remove fully reconstructed 3-body decays from background sample\newline (don't expect to be able to discriminate these)} + \item don't apply trigger prior to training + \end{itemize} + + \begin{exampleblock}{``blending'' technique} + \begin{itemize} + \item for each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, and one LD classifier + \item[$\Rightarrow$] 50 classifiers + \item one final MatrixNet classifier using the 13 base variables and the 50 classifiers as input + \newline(trained on the second $1/3$ of signal MC and the second $1/2$ of background MC) + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{performance} + \begin{itemize} + \item classifier prefers $\Ptau$ from prompt $\PDs$ + \end{itemize} + \begin{columns} + \begin{column}{.48\textwidth} + \begin{block}{MC response for different\newline $\Ptau$ production channels} + \includegraphics[width=.95\textwidth]{./for_paul.png} + \end{block} + \end{column} + \begin{column}{.48\textwidth} + \begin{block}{response for $\PDs\to\Pphi\Ppi$\newline data and MC} + \includegraphics[width=.95\textwidth]{./MN_BLEND_FLAT.png} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{calibration} + \begin{itemize} + \item assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time) + \item get correction $\PDs\leadsto\Ptau$ from MC + \item apply corrections to $\PDs\to\Pphi\Ppi$ on data + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC + \item until the very low likelihood end of the distribution + \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{MN_BLEND_FLAT.png} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item we used ProbNNmu already in the previous round of the analysis + \item now use MC12TuneV2 (latest) + \item two-fold reason:\begin{itemize} + \item expect better performance than CombDLL variables + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$) + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{PIDCalib} + \begin{itemize} + \item calibration strategy: use PIDCalib + \item confirm with $\PDs\to\Pphi\Ppi$ if everything is fine + \end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + cut\&fit: + \begin{itemize} + \item fit $\PDs\to\Pphi\Ppi$ with a TIS muon in data + \item cut on ProbNNmu of one muon + \item fit again + \item[$\rightarrow$] ratio is ``true'' cut efficiency + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=86.3\,\%$ + \end{block} + \end{column} + \begin{column}{.45\textwidth} + PIDCalib + \begin{itemize} + \item apply full selection (incl. trigger) to $\PDs\to\Pphi\Ppi$ MC reference sample + \item avoid IsMuon bias + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=89.8\,\%$ + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{?} + \begin{itemize} + \item first shown at \myhref{https://indico.cern.ch/event/291727/}{charming VRD meeting} + \item also mentionned at last \myhref{https://indico.cern.ch/event/298021/}{LHCb week} + \item many emails exchanged with Barbara Sciascia + \item mistakes on user side found + \item still no agreement + \end{itemize} + \begin{exampleblock}{phenomenologic treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$ + \end{itemize} + \end{exampleblock} + \begin{itemize} + \item planned: investigate further (usage/bug/samples) + \item planned: use muons from $\PDs\to\Pphi\Ppi$ directly + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{binning optimisation} + \begin{itemize} + \item how to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$ + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier + \item \textcolor{darkgreen}{now: optimise two-dimensions (optimise bin boundaries in both dimensions at the same time)} + \item unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain) + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{impact of new binning optimisation} + \begin{itemize} + \item removal of tiny bins which contribute negligible sensitivity + \item colour: limit obtained, using only this particular bin + \item number: rank of that bin (1=best sensitivity bin) + \end{itemize} + + ~ + + \begin{columns} + \begin{column}{.5\textwidth} + old analysis + + ~ + + \includegraphics[width=.95\textwidth]{./90CLonebinlimit.eps} + \end{column} + \begin{column}{.5\textwidth} + new analysis + + (2011 data, not final calibration) + \includegraphics[width=.95\textwidth]{./rank.eps} + \end{column} + \end{columns} + \end{frame} + + + \begin{frame} + \frametitle{mass shape} + \begin{itemize} + \item double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian) + \item fix fraction to ease calibration:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + calibrated $\Ptau$ mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + +\beamertemplateshadingbackground{darkgreen!30}{PineGreen!30} + \section{choice of triggers} + \begin{frame} + \frametitle{the story} + \begin{itemize} + \item first look at $\PDs\to\Pphi\Ppi$ revealed: signal/background much worse in 2012 + \item[$\rightarrow$] charm got more bandwidth in 2012 + \item taking all events quite unsatisfactory:\begin{itemize} + \item strictly speaking: we don't know why the events ended up on tape + \item trigger efficiencies unstable (TIS/TPS/TOS efficiencies for lots of lines and TCKs) + \item signal anyhow mostly TOS in a muon trigger + \end{itemize} + \item[$\Rightarrow$] if an event was background in the trigger, then don't consider it signal afterwards. + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{strategy} + \begin{itemize} + \item back of the envelope: limit scales with $1/\varepsilon_\text{sig}$ + \item back of the envelope: limit scales with $\sqrt{\varepsilon_\text{bkg}}$ + \item[$\Rightarrow$] minimise $FOM=\frac{\sqrt{\varepsilon_\text{bkg}}}{\varepsilon_\text{sig}}$ + \item running TCKsh and some combinatorics: $\mathcal{O}(2^{256}\approx 10^{75})$ possibilities of using HLT2 line (ignoring that there are different TCKs, TIS/TOS/TPS/DEC, \dots) + \item[$\rightarrow$] be more pragmatic! + \end{itemize} + \begin{exampleblock}{trigger optimisation} + \begin{itemize} + \item sort trigger lines (Punzi FoM) + \item start with events from the best trigger line and compute $FOM$ + \item add events from the next trigger and recompute $FOM$ + \item iterate and converge to $FOM(\text{all triggers})$ + \item use all triggers until $FOM$ starts rising. + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{our triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & || Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{$^1$ triggers in 2012} + \begin{itemize} + \item cuts changed through 2012 + \item[$\rightarrow$] \textcolor{darkgreen}{emulated two different TCKs for 2012} + \end{itemize} + \end{block}} + \only<2>{ + \begin{block}{$^2$ word on Hlt2DiMuonDetached} + \begin{itemize} + \item keep it simple here + \item line unchanged in 2012 + \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + \end{itemize} + \end{block}} + + \end{frame} + + \begin{frame} + \frametitle{cross check (not in the note)} + \begin{itemize} + \item shouldn't the multivariate classifier do better than any trigger? + \item back-of-the-envelope overestimates the improvement (expect $\sim 9\,\%$ improvement) + \item[$\rightarrow$] add events back to the ntuple, recalculate normalisation, redid fits + \item[$\Rightarrow$] \textcolor{darkgreen}{restricting the triggers gains $\sim 3\,\%$ sensitivity wrt.\ previous round} + \end{itemize} + \end{frame} +\beamertemplateshadingbackground{White}{White} + + \section{normalisation} + + \begin{frame} + \frametitle{relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012 + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} & 8.98 \pm 0.41 & 9.20 \pm 0.36\\ +\hline +\rm{\epsilon_{cal}}^{GEN} & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} & 9.794 \pm 0.028 & 9.134 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\Pphi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\Ptau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.95 \pm 0.12 & 2.05 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} & 35.45 \pm 0.11 \pm 0.14 & 39.1 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(\PDs\to\Pphi\Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\Ptau}_{\PDs} & 0.82 \pm 0.03 & 0.83 \pm 0.03 \\ +\hline +\mathcal{B}(\PDs\to\Ptau\Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.897 \pm 0.061 & 0.926 \pm 0.056 \\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6606 \pm 0.0059 & 0.527 \pm 0.041\\ +\hline +N_{norm} & 28,162 \pm 434 & 51,998 \pm 684\\ +\hline & \\[-1.5em]\hline +\alpha & (4.05 \pm 0.48) \times 10^{-9} & (1.83 \pm 0.25) \times 10^{-9}\\ +\alpha^{trash} & (7.90 \pm 0.49) \times 10^{-9} & (3.75 \pm 0.27) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{backgrounds} + + \begin{frame} + \frametitle{misidentification} + \begin{itemize} + \item most dominant: $\PDplus\to\PK\Ppi\Ppi$ + \item experience from last round: cut away low ProbNNmu range + \item check remaining data under $\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \item \textcolor{darkgreen}{$\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$ start to become visible in 2012} + \end{itemize} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{evil backgrounds} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy + \begin{itemize} + \item modelled in CONF note + \item optimised veto in PAPER + \item right now: both versions in the ANA note + \end{itemize} + \item baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$ + \begin{itemize} + \item fits better understood + \item sensitivity unchanged when removing veto + \item smaller uncertainty on expected background + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{remaining backgrounds} + \begin{itemize} + \item fit exponential to invariant mass spectrum in each likelihood bin + \item don't use $\pm \unit{30}{\MeV}$ in the fit + \item[$\rightarrow$] compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier developement} + \end{itemize} + {\begin{center} + most sensitive bins in 2011 and 2012 + \includegraphics[width=.4\textwidth]{./fit2011.png} + \includegraphics[width=.4\textwidth]{./fit2012.png} + \end{center}} + \end{frame} + + \section{results} + + \begin{frame} + \frametitle{expected limit} + \begin{itemize} + \item still blinded + \item consider nuisance parameters from background fit, signal pdf calibration, normalisation + \item nuisance parameters due to $\Ptau$ production not included in signal pdf shape, yet + \item limit for combined 2011+2012 analysis + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.6 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{./banana.png} + \end{frame} + +\beamertemplateshadingbackground{PineGreen!30}{White} + \section{model dependence} + + \begin{frame} + \frametitle{model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not applicable to New Physics with small $m_{\APmuon\Pmuon}$ + \item model independent description in \texttt{arXiv:0707.0988} + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms + \end{itemize} + \only<2->{ + \begin{itemize} + \item with radiative distribution limit gets worse by $51\,\%$ (dominantly from the $\Peta$ veto) + \item the other four Dalitz distributions behave nicely (within $7\,\%$) + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.eps} + \includegraphics[width=.331\textwidth]{./gammallrr.eps} + \includegraphics[width=.331\textwidth]{./gammarad.eps} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.eps} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.eps} +} + + \end{frame} + +\beamertemplateshadingbackground{White}{White} + + \begin{frame} + \frametitle{Conclusion} + \begin{columns} + \begin{column}{.55\textwidth} + \begin{itemize} + \item finally all pieces put together + \item model (in)dependence of $\Peta$ veto investigated + \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + \end{column} + \end{columns} + + \end{frame} + \end{document} diff --git a/FCC_LFV/trash.pdf b/FCC_LFV/trash.pdf new file mode 100644 index 0000000..8f7415e --- /dev/null +++ b/FCC_LFV/trash.pdf Binary files differ diff --git a/FCC_LFV/tungsten.png b/FCC_LFV/tungsten.png new file mode 100644 index 0000000..708e071 --- /dev/null +++ b/FCC_LFV/tungsten.png Binary files differ diff --git a/FCC_LFV/upsilon4s.png b/FCC_LFV/upsilon4s.png new file mode 100644 index 0000000..6921176 --- /dev/null +++ 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FIXME -\item Pefromed a toy study: -\begin{itemize} -\item Took SM MC, and apply the new highest odd acceptance from Christoph. -\item Divided into $3fb^{-1}$ corresponding samples -\item Used $2~GeV^2$ binning scenario. -\item Added two weights: new and old. -\item Recomputed observables for each toy using 2 acceptances. -\item Look into the differences. -\item Results in the next silde. -\end{itemize} - - - - - -\end{itemize} - - - - -\end{frame} - -\begin{frame}\frametitle{Numbers Fit, expected deviations} +\begin{frame}\frametitle{Numbers all around me...} \begin{tiny} -\begin{tabular}{c |c | c | c| c| c| c| c|} +\begin{tabular}{ |c |c | c | c| c| c| c| c|c|} \hline -$0.1 - 0.98$ & $0.0216008$ & $0.010946$ & $0.0404602$ & $0.0262259$ & $0.0233611$ & $0.0391067$ & $0.0120506$ \\ \hline -$1.1 - 2.5$ & $0.016072$ & $0.0053112$ & $0.0166444$ & $0.0126303$ & $0.0130115$ & $0.015087$ & $0.00553845$ \\ \hline -$2.5 -4$ & $0.0124394$ & $0.00424708$ & $0.011096$ & $0.00925205$ & $0.00799686$ & $0.00952774$ & $ 0.00424132$ \\ \hline -$4-6$ & $0.008646$ & $0.00312367$ & $0.0079593$ & $0.00727349$ & $0.00522152$ & $0.00651302$ & $0.00311269$ \\ \hline -$6-8$ & $0.015737$ & $0.00438532$ & $0.0100089$ & $0.0118984$ & $0.00831223$ & $0.009712$ & $0.00446352$ \\ \hline -$15 - 17$ & $0.0088157$ & $0.00366958 $ & $0.00542786$ & $0.00523935$ & $0.00441696$ & $0.00577158$ & $0.00269092$ \\ \hline -$17 - 19$ & $0.0271101$ & $0.0181168$ & $0.0237682$ & $0.0251109$ & $0.0172123$ & $0.0175126$ & $0.0105872$ \\ \hline - +{~} & \multicolumn{8}{|c|}{ number of sigmas} \\ \hline +$q^2 [GeV^2 /c^4]$ & $F_l$ & $S_3$ & $S_4$ & $S_5$ & $S_6$ & $S_7$ & $S_8$ & $S_9$ \\ \hline +$0.1 - 0.98$ & $2.05$ & $0.2$ & $0.61$ & $0.19$ & $1.05$ & $0.5$ & $0.58$ & $0.32$ \\ \hline +$1.1 - 2.5$ & $0.63$ & $0.8$ & $0.26$ & $1.19$ & $2.3$ & $0.78$ & $0.42$ & $0.65$ \\ \hline + \multicolumn{9}{|c|}{Not important bins} \\ \hline +$15 - 17$ & $0.06$ & $1.12$ & $0.89$ & $2.3$ & $0.67$ & $1.9$ & $0.7$ & $0.98$ \\ \hline +$17 - 19$ & $1.43$ & $2.5$ & $0.58$ & $0.41$ & $0.87$ & $1.29$ & $0.93$ & $0.915$ \\ \hline \end{tabular} \end{tiny} \end{frame} -\begin{frame}\frametitle{Numbers MoM, expected deviations } +\begin{frame}\frametitle{Systematics preliminary} +\begin{itemize} +\item Started accessing the systematics. +\item Look very reasonable: max=$\mathcal{O}(0.01)$ +\end{itemize} + + +\end{frame} +\begin{frame}\frametitle{Numbers all around me...} \begin{tiny} -\begin{tabular}{c |c | c | c| c| c| c| c|} +\begin{tabular}{ |c |c | c | c| c| c| c| c|c|} \hline - - -$0.1 - 0.98$ & $.01113$ & $0.0571538 $ & $0.484421$ & $0.875222$ & $0.750888$ & $0.808388$ & $0.110309$\\ \hline -$1.1- 2.5$ & $0.0233569$& $0.011525$ & $0.0567316$ & $0.0374716 $ & $0.0229218$ & $0.0227525$ & $0.00966214$ \\ \hline -$2.5-4$ & $0.0124508$ & $0.00714531$ & $0.0274325$ & $0.0486626$ & $0.0201143$ & $0.027187$ & $ 0.00653637$ \\ \hline -$4 - 6$ & $0.0125362$ & $0.00510912$ & $0.0490782$ & $0.0778953$ & $0.0117517$ & $0.0121875$ & $ 0.00381904$ \\ \hline -$6 - 8$ & $0.0694169$ & $0.0362361$ & $00.100802$ & $0.026377$ & $0.110168$ & $0.077164$ & $0.0304819$ \\ \hline -$15 - 17$ & $0.0547882$ & $0.00874876$ & $0.0129285$ & $0.0199238$ & $0.0047388$ & $0.00663897$ & $0.00431089$ \\ \hline -$17 - 19$ & $0.0365058$ & $0.0909971$ & $0.0113491$ & $0.0181383$ & $0.0414832$ & $0.0863238$ & $0.0135275$ \\ \hline - +{~} & \multicolumn{8}{|c|}{ absolute systematic} \\ \hline +$q^2 [GeV^2 /c^4]$ & $F_l$ & $S_3$ & $S_4$ & $S_5$ & $S_6$ & $S_7$ & $S_8$ & $S_9$ \\ \hline +$0.1 - 0.98$ & $0.02$ & $0.001$ & $0.008$ & $0.004$ & $007$ & $0.006$ & $0.002$ & $0.001$ \\ \hline +$1.1 - 2.5$ & $0.01$ & $0.004$ & $0.005$ & $0.003$ & $005$ & $0.004$ & $0.007$ & $0.004$ \\ \hline \end{tabular} \end{tiny} -\end{frame} +{~}\\ +Ok I don't want to type rest as I need to run high statistic toys, but they are all small =) -\begin{frame}\frametitle{Numbers I get on data} -\begin{itemize} -\item Q2= 0.1 0.98 delta Fl = -0.044327 Error: 0.0591652 Nsigma: -0.749208 -\end{itemize} - -\end{frame} - -%%%%%%%%%%%%%%%%%%%%%%% - -\begin{frame}\frametitle{Background conclusions} -To conclude: -\begin{itemize} -\item Preliminary. -\item There are to many hints of something being wrong. -\item I know some of you will say:"Statistically insignificant", but if you add them up you are looking at something that is starting to be significant. -\end{itemize} \end{frame} diff --git a/Kstmumu/TOYS_acc/Systematics.toc b/Kstmumu/TOYS_acc/Systematics.toc index b5401e1..20a70d8 100644 --- a/Kstmumu/TOYS_acc/Systematics.toc +++ b/Kstmumu/TOYS_acc/Systematics.toc @@ -1,3 +1,3 @@ \beamer@endinputifotherversion {3.24pt} \select@language {english} -\beamer@sectionintoc {1}{Background studies}{2}{0}{1} +\beamer@sectionintoc {1}{Background studies}{1}{0}{1} diff --git a/Lc23Mu/Status_report_04_02_15/Lc.aux b/Lc23Mu/Status_report_04_02_15/Lc.aux new file mode 100644 index 0000000..6704d6c --- /dev/null +++ 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+\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Status update o $\color{white}{\Lambda_c \rightarrow p \mu^- \mu^+}$]{Status update o $\color{white}{\Lambda_c \rightarrow p \mu^- \mu^+}$} +\author{Marcin Chrz\k{a}szcz$^{1}$, Tadeusz Lesiak$^{2}$, Mariusz Witek$^{2}$,\\ Borys Nowak$^{2}$} +\institute{$^1$~University of Zurich,\\ $^{2}$ Institute of nuclear Physics} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +\institute{~(UZH)} + +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Motivation} +\begin{frame}\frametitle{Why to search for $\Lambda_c \to \Pproton \mu^{+} \mu^{-}$?} + + +\begin{itemize} +\item Decay of $\Lambda_c^+ \to \Pproton \mu^+ \mu^-$ is a FCNC. +\item Extremely suppressed in SM due to GIM mechanism. +\item We will use the experience from $\tau \to \Pproton \mu \mu$. + +\end{itemize} + +\begin{columns} +\column{2.5in} +\begin{center} +\includegraphics[scale=0.18]{new/FCNC.png} +\end{center} +~$\mathcal{B}( \Lambda_c^{+} \to p \mu^{-} \mu^{+} ) < 4.4 \times 10^{-5}$\\ + ~ \@ 90\% CL arXiv:1107.4465 + +\column{3.5in} +\includegraphics[scale=0.2]{babar.png}\\ +Yield: $11.1 \pm 5.0 \pm 2.5$ + +\end{columns} + +We should easily beat Babar. + + +\end{frame} + +\begin{frame}\frametitle{Preliminary selection } + +\begin{columns} +\column{2.5in} +~Stripping: +\begin{itemize} +\item $\rm{PID}(\mu)>-5$, $\rm{PID}(\Pproton) >10$ +\item $\rm{IPCHi2}>9$, $\rm{PID}(\mu -K)>0$, $\rm{GHOST}<0.3$, $\rm{PID}(\Pproton)>10$, $Pt>300$ +\item $\Delta m<150MeV$ +\item $c\tau >100\mu m$ +\item $\rm{IPChi2} < 225$ +\end{itemize} +~Additional: +\begin{itemize} +\item Blind region $\vert m(p\mu\mu) - 2286.46 \vert <40 MeV$. +\item $\phi$, $\omega$ veto. +\end{itemize} +\column{3.5in} + +\includegraphics[scale=0.18]{new/Lc_mass.png}\\ + + + + + +\includegraphics[scale=0.2]{new/blind.png}\\ + +\end{columns} + + + + +\end{frame} + + +\section{Strategy} +\begin{frame} + +\frametitle{Strategy} +{~} +Follow the strategy of $\tau$ analysis: +\begin{itemize} +\item Take prompt $\Lambda_c$, separate approach to SL. +\item Loose cut preselection. +\item Train MVA on MC prompt signal and recalibrate on data. +\item Calibrate on date. +\item Normalize to $\Lambda_c^{+} \to \Pproton K^{-} \pi^{+}$, $\Lambda_c^{+} \to \Pproton \pi^{-} \pi^{+}$ or $\Lambda_c \to \Pproton \phi(\mu \mu)$. +\item Optimise the binning in MVA. +\item CLs method for limit. +\end{itemize} + +\end{frame} + +\section{Normalization channel} +\begin{frame}\frametitle{Normalization channel} +\begin{itemize} +\item We have 3 candidates for normalization channel. +\begin{enumerate} +\item $\Lambda_c \to \Pproton \phi(\mu \mu)$, $BR= (2.4 \pm 0.8) \times 10^{-7} $ +\item $\Lambda_c^{+} \to \Pproton K^{-} \pi^{+}$, $BR= (5.0 \pm 1.3) \times 10^{-2} $ +\item $\Lambda_c^{+} \to \Pproton \pi^{-} \pi^{+}$, $BR= (3.5 \pm 2.0) \times 10^{-3} $ +\end{enumerate} +From above list $\Lambda_c \to \Pproton \phi(\mu \mu)$ is a perfect candidate for normalization. +However Br is a bit low. + + + +\end{itemize} + + + + +\end{frame} + + + + +\begin{frame}\frametitle{Optimising the selection} +\begin{columns} +\column{2.5in} +\begin{itemize} +\item Last time for studies we used BDT that was trained on the fly. +\item Now a student produced a new optimised BDT +\item I include his thesis as attachment to this presentation. +\end{itemize} + + +\column{2.5in} +\includegraphics[width=0.95\textwidth]{images/roc.png}\\ + +\end{columns} + + +\end{frame} + + + + +\begin{frame}\frametitle{Comments about the BDT} + +\begin{itemize} +\item From historical reasons we are training this classifier on MC vs MC +\item Problematic part is that we have limited MC background sample. +\item We have how ever the opposite sign (OS) channel: $\PLambdac \to \APproton \APmuon \APmuon$ +\item The obvious idea was to use this as an background extrapolation and use it for training and optimisation. +\end{itemize} + + +\end{frame} + +\begin{frame}\frametitle{Differences between SS and opposite sign data} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.95\textwidth]{borys/v_Lambda_cplus_FD_OWNPV_2011_MD.pdf}\\ +\includegraphics[width=0.95\textwidth]{borys/v_Lambda_cplus_PT_2011_MD.pdf}\\ +\column{2.5in} +\includegraphics[width=0.95\textwidth]{borys/v_mu_two_PT_2011_MD.pdf}\\ +\includegraphics[width=0.95\textwidth]{borys/v_proton_PT_2011_MD.pdf} + +\end{columns} + + +\end{frame} + +\begin{frame}\frametitle{Normalization channel} +\begin{columns} + +\column{2.6in} +\begin{itemize} +\item $\mathcal{O}(500)$ events in pour dataset. +\item Can be used for normalization! +\item With the new BDT we also see small peak of $\Pomega$ +\item Will veto that. +\end{itemize} +\column{2.5in} +\includegraphics[scale=0.17]{new/Lc_mass_b.png}\\ +\includegraphics[scale=0.17]{new/Lc_mass.png} + +\end{columns} + + + + +\end{frame} + + +\begin{frame}\frametitle{Possible background} + +\begin{center} + + \begin{tabular}{| c | c | c |} + \hline + \textbf{ Resonance} & $\mathcal{B} (\Lambda_c \to p X)$& $\mathcal{B} (X \to \mu \mu)$\\ \hline + + $\eta$ & UNKNOWN & $(5.8 \pm 0.6) \times 10^{-6}$ \\ \hline + $\rho^0$ & UNKNOWN & $(4.55 \pm 0.28) \times 10^{-5}$ \\ \hline + $\omega$ & UNKNOWN & $(9.1 \pm 3.0) \times 10^{-5}$ \\ \hline + $f(980)$ & $(2.8 \pm 1.9) \times 10^{-3}$ & UNKNOWN \\ \hline + $\phi$ & $(8.2 \pm 2.7) \times 10^{-4} $ & $(2.89 \pm 0.19) \times 10^{-4}$ \\ \hline \hline + + \textbf{ Resonance} & $\mathcal{B} (\Lambda_c \to p X)$ & $\mathcal{B} (X \to \mu \mu \gamma)$\\ \hline + $\eta$ & UNKNOWN & $(3.1 \pm 0.4) \times 10^{-4}$ \\ \hline + \end{tabular} +\end{center} + + + + + +\end{frame} + + + +\section{Summary} +\begin{frame}\frametitle{Summary} + +\begin{itemize} +\item Looks like we will have limits $\mathcal{O}(10^{-8})$ +\item We already see a new $\Lambda_c \to \omega \Pproton$ decay, needs separate analysis +\item Normalization channel is still open, but we are converging towards $\Lambda_c^{+} \to \Pproton \pi^{-} \pi^{+}$ +\item We have one tight cut on the stripping (flight distance), we are considering several solutions. + +\end{itemize} + + + +\end{frame} + + +\end{document} diff --git a/Lc23Mu/Status_report_04_02_15/Lc.toc b/Lc23Mu/Status_report_04_02_15/Lc.toc new file mode 100644 index 0000000..6032ee7 --- /dev/null +++ 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+%\DeclareCaptionFont{uiblack}{\color{uiblack}} +%\DeclareCaptionFont{uipoppy}{\color{uipoppy}} +%\captionsetup{labelfont={uipoppy},textfont=uiblack} + +% see the macros.tex file for definitions +%\include{macros } + +% title slide definition +\title{FCNF and L/BNV \\in $\Lambda_c$ decays} +%\subtitle{a bias report} +\author{ \underline{Marcin Chrz\k{a}szcz}$^{1,2}$, Tadeusz Lesiak$^{1}$, Mariusz Witek$^{1}$ } +\institute[UTH] +{ + %\begin{tiny} + $ ^1$ Institute of Nuclear Physics, Krakow,\\ +$ ^2$ University of Zurich + + + %\end{tiny}smallsmall +} + + +\date{ \begin{small} $12^{th}$ Feb 2014 \end{small}} + +%-------------------------------------------------------------------- +% Introduction +%-------------------------------------------------------------------- + +\begin{document} + + + + +\setbeamertemplate{background} +{\includegraphics[width=\paperwidth,height=\paperheight]{frontpage_bg_mine}} +\setbeamertemplate{footline}[default] + +\begin{frame} +\vspace{1.1cm} +\begin{columns} +\column{2.75in} + \titlepagem + + \begin{center} + \includegraphics[height=1.0cm ]{pic/uzh.jpg} + % \hspace{0.5cm} + % \includegraphics[height=1.5cm]{pic/babar.jpg} + \hspace{1cm} + \includegraphics[height=1.0cm]{pic/ifj.png} + \hspace{1cm} + %\includegraphics[height=1.0cm]{pic/SNS.jpg} + \end{center} + \vspace{10cm} +\column{2.0in} +\end{columns} +\end{frame} + +%-------------------------------------------------------------------- +% OUTLINE +%-------------------------------------------------------------------- + + + + +\section[Outline]{} +\begin{frame} +\tableofcontents +\end{frame} + + + + + + + +%------------------------------------------------------------------- +% Introduction +%------------------------------------------------------------------- +% +% Set the background for the rest of the slides. +% Insert infoline +\setbeamertemplate{background} + {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +\setbeamertemplate{footline}[bunsentheme] + +\title{Report on $\tau \to p \Plepton \Plepton$} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\setbeamertemplate{background} + {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}} +\setbeamertemplate{footline}[bunsentheme] +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%2>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Motivation} +\begin{frame}\frametitle{Why to search for $\Lambda_c \to \Pproton \mu^{+} \mu^{-}$?} + + +\begin{itemize} +\item Decay of $\Lambda_c^+ \to \Pproton \mu^+ \mu^-$ is a FCNC. +\item Extremely suppressed in SM due to GIM mechanism. +\item We will use the experience from $\tau \to \Pproton \mu \mu$. + +\end{itemize} + +\begin{columns} +\column{2.5in} +\begin{center} +\includegraphics[scale=0.18]{new/FCNC.png} +\end{center} +~$\mathcal{B}( \Lambda_c^{+} \to p \mu^{-} \mu^{+} ) < 4.4 \times 10^{-5}$\\ + ~ \@ 90\% CL arXiv:1107.4465 + +\column{3.5in} +\includegraphics[scale=0.2]{babar.png}\\ +Yield: $11.1 \pm 5.0 \pm 2.5$ + +\end{columns} + +We should easily beat Babar. + + +\end{frame} + +\section{Strategy} +\begin{frame} + +\frametitle{Strategy} +{~} +Follow the strategy of $\tau$ analysis: +\begin{itemize} +\item Take prompt $\Lambda_c$, separate approach to SL. +\item Loose cut preselection. +\item Train MVA on MC prompt signal and recalibrate on data. +\item Calibrate on date. +\item Normalize to $\Lambda_c^{+} \to \Pproton K^{-} \pi^{+}$, $\Lambda_c^{+} \to \Pproton \pi^{-} \pi^{+}$ or $\Lambda_c \to \Pproton \phi(\mu \mu)$. +\item Optimise the binning in MVA. +\item CLs method for limit. +\end{itemize} + +\end{frame} + +\section{Normalization channel} +\begin{frame}\frametitle{Normalization channel} +\begin{itemize} +\item We have 3 candidates for normalization channel. +\begin{enumerate} +\item $\Lambda_c \to \Pproton \phi(\mu \mu)$, $BR= (2.4 \pm 0.8) \times 10^{-7} $ +\item $\Lambda_c^{+} \to \Pproton K^{-} \pi^{+}$, $BR= (5.0 \pm 1.3) \times 10^{-2} $ +\item $\Lambda_c^{+} \to \Pproton \pi^{-} \pi^{+}$, $BR= (3.5 \pm 2.0) \times 10^{-3} $ +\end{enumerate} +From above list $\Lambda_c \to \Pproton \phi(\mu \mu)$ is a perfect candidate for normalization. +However Br is a bit low. + + + +\end{itemize} + + + + +\end{frame} + + + +\begin{frame}\frametitle{First look in data I} +\begin{columns} + +\column{2.6in} +\begin{itemize} +\item With some PID and vertex cuts we can see our $\Lambda_c \to \Pproton \phi(\mu \mu)$ +\item Back of the envelope calculations predict we should have 400 of those events in $3fb^{-1}$ +\item A bit small for normalization. +\end{itemize} +\column{2.5in} +\includegraphics[scale=0.17]{new/Lc_mass_b.png}\\ +\includegraphics[scale=0.17]{new/Lc_mass.png} + +\end{columns} + + + + +\end{frame} + + +\begin{frame}\frametitle{Possible background} + +\begin{center} + + \begin{tabular}{| c | c | c |} + \hline + \textbf{ Resonance} & $\mathcal{B} (\Lambda_c \to p X)$& $\mathcal{B} (X \to \mu \mu)$\\ \hline + + $\eta$ & UNKNOWN & $(5.8 \pm 0.6) \times 10^{-6}$ \\ \hline + $\rho^0$ & UNKNOWN & $(4.55 \pm 0.28) \times 10^{-5}$ \\ \hline + $\omega$ & UNKNOWN & $(9.1 \pm 3.0) \times 10^{-5}$ \\ \hline + $f(980)$ & $(2.8 \pm 1.9) \times 10^{-3}$ & UNKNOWN \\ \hline + $\phi$ & $(8.2 \pm 2.7) \times 10^{-4} $ & $(2.89 \pm 0.19) \times 10^{-4}$ \\ \hline \hline + + \textbf{ Resonance} & $\mathcal{B} (\Lambda_c \to p X)$ & $\mathcal{B} (X \to \mu \mu \gamma)$\\ \hline + $\eta$ & UNKNOWN & $(3.1 \pm 0.4) \times 10^{-4}$ \\ \hline + \end{tabular} +\end{center} + + + + + +\end{frame} + + + +\begin{frame}\frametitle{First look in data II } +\begin{columns} + +\column{2.6in} +\begin{itemize} +\item We also have looked at dimuon spectrum. +\item Clearly $\phi$, $\eta$, $\omega$ visible. +\item We also see in data $\Lambda_c \to \omega(\mu \mu) \Pproton$. +\end{itemize} +\column{2.5in} +\includegraphics[scale=0.12]{new/bck.png}\\ + + +\end{columns} + + + + +\end{frame} + +\section{MVA} +\begin{frame}\frametitle{Preliminary selection } + +\begin{columns} +\column{2.5in} +~Stripping: +\begin{itemize} +\item PID($\mu$)>-5, PID($\Pproton$) >10 +\item IPCHi2>9, PID($\mu -K$)>0, GHOST<0.3, PID($\Pproton$)>10, Pt>300 +\item $\Delta m<150MeV$ +\item $c\tau >100\mu m$ +\item $IPChi2 < 225$ +\end{itemize} +~Additional: +\begin{itemize} +\item Blind region $\vert m(p\mu\mu) - 2286.46 \vert <20 MeV$. +\item $\phi$, $\omega$ veto. +\end{itemize} +\column{3.5in} + +\includegraphics[scale=0.18]{new/Lc_mass.png}\\ + + + + + +\includegraphics[scale=0.2]{new/blind.png}\\ + +\end{columns} + + + + +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 + + + +\begin{frame}\frametitle{Preliminary TMVA} +\begin{columns} + +\column{2.8in} +\begin{itemize} +\item Variables adopted form $\tau \to 3\mu$(see Marta's talk). +\item In the future we will use Blending for the classifiers. +\item Already thanks to this BDTG we can pick up $\Lambda_c\ \to \omega(\mu\mu) \Pproton$. + +\end{itemize} +\includegraphics[scale=0.2]{new/omega.png} +\column{2.5in} +\includegraphics[scale=0.2]{new/overtrain_BDTG.jpg}\\ +\includegraphics[scale=0.2]{new/rejBvsS.jpg} + +\end{columns} + + + +\end{frame} + + +\section{Summary} +\begin{frame}\frametitle{Summary} + +\begin{itemize} +\item Looks like we will have limits $\mathcal{O}(10^{-7})$ - $\mathcal{O}(10^{-8})$ +\item We already see a new $\Lambda_c \to \omega \Pproton$ decay! +\item Normalization channel is still open, but we are converging towards $\Lambda_c^{+} \to \Pproton \pi^{-} \pi^{+}$ +\item We have one tight cut on the stripping (flight distance), we are considering several solutions. + +\end{itemize} + + + +\end{frame} +\end{document} diff --git a/Lc23Mu/Status_report_04_02_15/Lc2pll.toc b/Lc23Mu/Status_report_04_02_15/Lc2pll.toc new file mode 100644 index 0000000..6104b69 --- /dev/null +++ b/Lc23Mu/Status_report_04_02_15/Lc2pll.toc @@ -0,0 +1,7 @@ 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to use, copy, modify, merge, publish, +distribute, sublicense, and/or sell copies of the Software, and to +permit persons to whom the Software is furnished to do so, subject to +the following conditions: + +The above copyright notice and this permission notice shall be +included in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE +LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION +OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION +WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. diff --git a/Lc23Mu/Status_report_04_02_15/macros.aux b/Lc23Mu/Status_report_04_02_15/macros.aux new file mode 100644 index 0000000..1420aa7 --- /dev/null +++ b/Lc23Mu/Status_report_04_02_15/macros.aux @@ -0,0 +1,27 @@ +\relax +\@setckpt{macros}{ +\setcounter{page}{1} +\setcounter{equation}{0} +\setcounter{enumi}{0} +\setcounter{enumii}{0} +\setcounter{enumiii}{0} +\setcounter{enumiv}{0} +\setcounter{footnote}{0} +\setcounter{mpfootnote}{0} +\setcounter{beamerpauses}{0} +\setcounter{bookmark@seq@number}{0} +\setcounter{lecture}{0} +\setcounter{part}{0} +\setcounter{section}{0} +\setcounter{subsection}{0} +\setcounter{subsubsection}{0} +\setcounter{subsectionslide}{0} +\setcounter{framenumber}{0} +\setcounter{figure}{0} 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dauIter()) ) { +// something not impotent ... + if(FSR) + { + if( dau->pdtEntry() != 0 ) + { + string name( dau->pdtEntry()->name() ); + if( name.find( "gamma" ) != string::npos){ + std::cout<<"SUCCESSSSS!!!!!!!, we found gamma"< +Babel and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, farsi, arabic, croatian, bulgarian, ukrainian, russian, czech, slov +ak, danish, dutch, finnish, french, basque, ngerman, german, german-x-2009-06-1 +9, ngerman-x-2009-06-19, ibycus, monogreek, greek, ancientgreek, hungarian, san +skrit, italian, latin, latvian, lithuanian, mongolian2a, mongolian, bokmal, nyn +orsk, romanian, irish, coptic, serbian, turkish, welsh, esperanto, uppersorbian +, estonian, indonesian, interlingua, icelandic, kurmanji, slovenian, polish, po +rtuguese, spanish, galician, catalan, swedish, ukenglish, pinyin, loaded. +(/usr/share/texmf/tex/latex/beamer/base/beamer.cls +(/usr/share/texmf/tex/latex/beamer/base/beamerbasercs.sty +Package: beamerbasercs 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b/Zurich_group/03_04_2015/Systematics.tex @@ -0,0 +1,79 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[$\PBzero \to \PKstar \Pmu \Pmu$ anomaly]{$\PBzero \to \PKstar \Pmu \Pmu$ anomaly} +\author{Marcin Chrz\k{a}szcz$^{1}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz{~}} +\institute{(UZH)} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- +\begin{frame}\frametitle{Unblinded results} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/FLPad.pdf} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/AFBPad.pdf} +\end{columns} +\end{frame} + +\begin{frame}\frametitle{Unblinded results} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/FLPad.pdf} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/AFBPad.pdf} +\end{columns} +\end{frame} + +\begin{frame}\frametitle{Unblinded results} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/S3Pad.pdf} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/S4Pad.pdf} +\end{columns} +\end{frame} + +\begin{frame}\frametitle{Unblinded results} +\begin{columns} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/S5Pad.pdf} +\column{2.5in} +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/S7Pad.pdf} +\end{columns} +\end{frame} + + \begin{frame}\frametitle{Unblinded results} + +\includegraphics[width=0.9\textwidth]{Kstarmumu_plots/P5pPadCompare2011.pdf} + +\end{frame} + + + +\end{document} diff --git a/Zurich_group/03_04_2015/Systematics.tex~ b/Zurich_group/03_04_2015/Systematics.tex~ new file mode 100644 index 0000000..e101957 --- /dev/null +++ b/Zurich_group/03_04_2015/Systematics.tex~ @@ -0,0 +1,141 @@ +\documentclass[xcolor=svgnames]{beamer} +\usepackage[utf8]{inputenc} +\usepackage[english]{babel} +\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} + +\title[Angular distribution of background]{Angular distribution of background} +\author{Marcin Chrz\k{a}szcz$^{1,2}$, Nicola Serra$^{1}$} +\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow} +\date{\today} + +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{diagram.png}\\ + +\end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}\frametitle{Quo vadis $\PBzero \to \PKstar \mu \mu$?} + +\center \includegraphics[width=0.8\paperwidth]{sys.png}\\ + +\end{frame} + + +\section{Introduction} +\begin{frame}\frametitle{Assumptions} +\begin{columns} +\column{3in} +\begin{itemize} +\item Each method assumes that background angular distribution is the same in the red and green region. +\item This might not be necessary the true. +\item Let's test this using method of moments. +\end{itemize} +\column{2.5in} + +\includegraphics[width=0.8\textwidth]{mass2.png}\\ + +\end{columns} + + +\end{frame} + +\begin{frame}\frametitle{Studied background region} +{~} + +\begin{columns} + +\column{2.5in} +\begin{itemize} +\item Divided mass regions in different $q^2$ bins. +\item To each calculate the $S_x$ components and see if there is a clear trend. +\item Try fitting and seeing the impact in the signal window. +\end{itemize} + + +\column{2.5in} +\includegraphics[scale=0.22]{plots2/PLOT.png} +\end{columns} + + +\end{frame} + +\begin{frame}\frametitle{Studied background region} +{~} + +\begin{columns} + +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_Fl1.png}\\ +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_Fl2.png}\\ +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_Fl3.png}\\ + +\end{columns} +\begin{columns} + +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_Fl4.png}\\ +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_S3.png}\\ +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_S4.png}\\ + +\end{columns} + +\end{frame} + +\begin{frame}\frametitle{Studied background region} +{~} + +\begin{columns} + +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_S5.png}\\ +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_S6s.png}\\ +\column{1.66in} +\includegraphics[width=0.95\textwidth]{plots_folder/Q0_1_0_98_S7.png}\\ + +\end{columns} +\begin{columns} 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/AvantGarde-Book /AvantGarde-BookOblique /AvantGarde-Demi /AvantGarde-DemiOblique /Bookman-Demi /Bookman-DemiItalic /Bookman-Light + /Bookman-LightItalic /Helvetica-Narrow /Helvetica-Narrow-Bold /Helvetica-Narrow-BoldOblique /Helvetica-Narrow-Oblique /NewCenturySchlbk-Roman /NewCenturySchlbk-Bold /NewCenturySchlbk-BoldItalic /NewCenturySchlbk-Italic /Palatino-Bold + /Palatino-BoldItalic /Palatino-Italic /Palatino-Roman ] {ISOLatin1Encoding reEncode } forall +%%EndProlog +%%BeginSetup +%%EndSetup +newpath gsave .25 .25 scale gsave 0 0 t black[ ] 0 sd 6 lw 1 1 1 c 2268 1538 0 0 bf black 1 1 1 c 1678 1154 363 261 bf black 1678 1154 363 261 bl 1 1 1 c 0.677317 0.0682927 0 c 6 4 1006 277 bf 0.665366 0.0634146 0 c 5 4 1012 277 bf 0.653415 + 0.0585366 0 c 6 4 1017 277 bf 0.641463 0.0536585 0 c 5 4 1023 277 bf 6 4 1028 277 bf 0.629512 0.0487805 0 c 6 4 1034 277 bf 0.617561 0.0439024 0 c 5 4 1040 277 bf 6 4 1045 277 bf 0.60561 0.0390244 0 c 5 4 1051 277 bf 0.593659 0.0341463 0 c 6 4 1056 + 277 bf 6 4 1062 277 bf 0.581707 0.0292683 0 c 5 4 1068 277 bf 6 4 1073 277 bf 0.569756 0.0243902 0 c 5 4 1079 277 bf 6 4 1084 277 bf 0.557805 0.0195122 0 c 6 4 1090 277 bf 5 4 1096 277 bf 0.545854 0.0146341 0 c 6 4 1101 277 bf 5 4 1107 277 bf 6 4 + 1112 277 bf 6 4 1118 277 bf 5 4 1124 277 bf 0.533902 0.0097561 0 c 6 4 1129 277 bf 5 4 1135 277 bf 6 4 1140 277 bf 6 4 1146 277 bf 0.521951 0.00487805 0 c 5 4 1152 277 bf 6 4 1157 277 bf 5 4 1163 277 bf 6 4 1168 277 bf 6 4 1174 277 bf 5 4 1180 277 + bf 6 4 1185 277 bf 5 4 1191 277 bf 6 4 1196 277 bf 5 4 1202 277 bf 6 4 1207 277 bf 6 4 1213 277 bf 5 4 1219 277 bf 6 4 1224 277 bf 5 4 1230 277 bf 6 4 1235 277 bf 6 4 1241 277 bf 5 4 1247 277 bf 6 4 1252 277 bf 0.533902 0.0097561 0 c 5 4 1258 277 bf + 6 4 1263 277 bf 6 4 1269 277 bf 5 4 1275 277 bf 0.545854 0.0146341 0 c 6 4 1280 277 bf 5 4 1286 277 bf 6 4 1291 277 bf 6 4 1297 277 bf 5 4 1303 277 bf 0.557805 0.0195122 0 c 6 4 1308 277 bf 5 4 1314 277 bf 0.569756 0.0243902 0 c 6 4 1319 277 bf 6 4 + 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{mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def +/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def +/reEncode {exch findfont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse } forall /Encoding exch def currentdict end dup /FontName get exch definefont pop } def [/Times-Bold /Times-Italic /Times-BoldItalic /Helvetica /Helvetica-Oblique + /Helvetica-Bold /Helvetica-BoldOblique /Courier /Courier-Oblique /Courier-Bold /Courier-BoldOblique /Times-Roman /AvantGarde-Book /AvantGarde-BookOblique /AvantGarde-Demi /AvantGarde-DemiOblique /Bookman-Demi /Bookman-DemiItalic /Bookman-Light + /Bookman-LightItalic /Helvetica-Narrow /Helvetica-Narrow-Bold /Helvetica-Narrow-BoldOblique /Helvetica-Narrow-Oblique /NewCenturySchlbk-Roman /NewCenturySchlbk-Bold /NewCenturySchlbk-BoldItalic /NewCenturySchlbk-Italic /Palatino-Bold + /Palatino-BoldItalic /Palatino-Italic /Palatino-Roman ] {ISOLatin1Encoding reEncode } forall +%%EndProlog +%%BeginSetup +%%EndSetup +newpath 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pop +} def +% +%gsave abs CLW add /a ED a 0 dtransform round exch round exch +%2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +%% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +%% DG/SR modification end +%Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +%/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +%% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +%% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +%% def +%a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +%pop pop } def +%% DG/SR modification end +% +/BeginArrow { + ADict begin % hold it local, for end see EndArrow + /@mtrx CM def + gsave + 2 copy T + 2 index sub neg exch + 3 index sub exch Atan + rotate newpath +} def +% +/EndArrow { @mtrx setmatrix CP 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def + x neg y moveto + x neg CLW 2 div L x CLW 2 div L x y L stroke + 0 CLW moveto +} def +% +/RoundBracket { + CLW mul add dup 2 div + /x ED mul /y ED /mtrx CM def + 0 CLW 2 div T x y mul 0 ne { x y scale } if + 1 1 moveto + .85 .5 .35 0 0 0 curveto + -.35 0 -.85 .5 -1 1 curveto + mtrx setmatrix stroke 0 CLW moveto +} def +% +/SD { 0 360 arc fill } def +% +/EndDot { % DS is the dot size + { /z DS def } { /z 0 def } ifelse + /b ED 0 z DS SD b { 0 z DS CLW sub SD } if + 0 DS z add CLW 4 div sub moveto } def +% +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { + /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto + load } if ] cvx newpath 3 1 roll T exec } def +% +%/NArray { +% aload length 2 div dup dup cvi eq not { exch pop } if /n exch +% cvi def +%} def +% +/NArray { % holds the coordinates and on top of stack the showpoints boolean + /showpoints ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + showpoints { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/Line { + NArray n 0 eq not + { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def + n { Lineto } repeat + CP 4 2 roll ArrowB L pop pop + } if +} def +% +/Arcto { + /a [ 6 -2 roll ] cvx def + a r + /arcto load stopped { 5 } { 4 } ifelse { pop } repeat + a +} def +% +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq + and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } + repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 + ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 + moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto + Lineto pop pop closepath } ifelse } def +/Diamond { + /mtrx CM def + T rotate + /h ED + /w ED + dup 0 eq { pop } { CLW mul neg + /d ED + /a w h Atan def + /h d a sin Div h add def + /w d a cos Div w add def } ifelse + mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div + /ArrowA { moveto } def + /ArrowB { } def + false Line + closepath mtrx setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +% +/Triangle { + /mtrx CM def + translate + rotate /h ED 2 div /w ED + dup CLW mul /d ED + /h h d w h Atan sin Div sub def + /w w d h w Atan 2 div dup cos exch sin Div mul sub def + mark + 0 d w neg d 0 h w d 0 d + /ArrowA { moveto } def + /ArrowB { } def + false + Line + closepath + mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def + setmatrix pop +} def +% DG/SR modification end +% +/CCA { + /y ED /x ED + 2 copy y sub /dy1 ED + x sub /dx1 ED + /l1 dx1 dy1 Pyth def +} def +% +/CC { + /l0 l1 def + /x1 x dx sub def + /y1 y dy sub def + /dx0 dx1 def + /dy0 dy1 def + CCA + /dx dx0 l1 c exp mul dx1 l0 c exp mul add def + /dy dy0 l1 c exp mul dy1 l0 c exp mul add def + /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def + /x2 x l0 dx mul m mul sub def + /y2 y l0 dy mul m mul sub def + /dx l1 dx mul m mul neg def + /dy l1 dy mul m mul neg def +} def +% +/IC { + /c c 1 add def + c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse + /a a 2 mul 3 div 45 cos b exp div def + CCA + /dx 0 def + /dy 0 def +} def +% +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +% +/OpenCurve { + NArray n 3 lt + { n { pop pop } repeat } + { BOC /n n 3 sub def n { NC } repeat EOC } ifelse +} def +% +/AltCurve { + { false NArray n 2 mul 2 roll + [ n 2 mul 3 sub 1 roll ] aload + /Points ED + n 2 mul -2 roll } + { false NArray } ifelse + n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse +} def +% +/ClosedCurve { + NArray n 3 lt + { n { pop pop } repeat } + { n 3 gt { CheckClosed } if + 6 copy n 2 mul 6 add 6 roll + IC CC x y moveto n { NC } repeat + closepath pop pop + } ifelse +} def +% +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def +% +/FontDot { + DS 2 mul dup + matrix scale matrix concatmatrix exch matrix + rotate matrix concatmatrix exch + findfont exch makefont setfont +} def +% +/Rect { + x1 y1 y2 add 2 div moveto + x1 y2 lineto + x2 y2 lineto + x2 y1 lineto + x1 y1 lineto + closepath +} def +% +/OvalFrame { + x1 x2 eq y1 y2 eq or + { pop pop x1 y1 moveto x2 y2 L } + { y1 y2 sub abs x1 x2 sub abs 2 copy gt + { exch pop } { pop } ifelse + 2 div exch { dup 3 1 roll mul exch } if + 2 copy lt { pop } { exch pop } ifelse + /b ED + x1 y1 y2 add 2 div moveto + x1 y2 x2 y2 b arcto + x2 y2 x2 y1 b arcto + x2 y1 x1 y1 b arcto + x1 y1 x1 y2 b arcto + 16 { pop } repeat + closepath + } ifelse +} def +% +/Frame { + CLW mul /a ED + 3 -1 roll + 2 copy gt { exch } if + a sub /y2 ED + a add /y1 ED + 2 copy gt { exch } if + a sub /x2 ED + a add /x1 ED + 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse +} def +% +/BezierNArray { + /f ED + counttomark 2 div dup cvi /n ED + n eq not { exch pop } if + n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat + f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse +} def +% +/OpenBezier { + BezierNArray + n 1 eq + { pop pop } + { ArrowA n 4 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + 6 2 roll 4 2 roll ArrowB curveto } ifelse +} def +% +/ClosedBezier { + BezierNArray + n 1 eq + { pop pop } + { moveto n 1 sub 3 idiv + { 6 2 roll 4 2 roll curveto } repeat + closepath } ifelse +} def +% +/BezierShowPoints { + gsave + Points aload length 2 div cvi /n ED + moveto + n 1 sub { lineto } repeat + CLW 2 div SLW [ 4 4 ] 0 setdash stroke + grestore +} def +% +/Parab { + /y0 ED /x0 ED /y1 ED /x1 ED + /dx x0 x1 sub 3 div def + /dy y0 y1 sub 3 div def + x0 dx sub y0 dy add x1 y1 ArrowA + x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB + curveto + /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def +} def +% +/Grid { + newpath + /a 4 string def + /b ED /c ED /n ED + cvi dup 1 lt { pop 1 } if + /s ED + s div dup 0 eq { pop 1 } if + /dy ED s div dup 0 eq { pop 1 } if + /dx ED dy div round dy mul + /y0 ED dx div round dx mul + /x0 ED dy div round cvi + /y2 ED dx div round cvi + /x2 ED dy div round cvi + /y1 ED dx div round cvi + /x1 ED + /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def + /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def + b 0 gt { + /z1 b 4 div CLW 2 div add def +% /Helvetica findfont b scalefont setfont + /b b .95 mul CLW 2 div add def } if + systemdict /setstrokeadjust known + { true setstrokeadjust /t { } def } + { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add + exch itransform } bind def } ifelse + gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse + /i x1 def + /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def + /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def + x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if + { i dx mul dup y0 moveto + b 0 gt + { gsave c i a cvs dup stringwidth pop + /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse + h 0 gt {b neg}{z1} ifelse + rmoveto show grestore } if + dup t f moveto + g t L stroke + /i i w add def + } repeat + grestore + gsave + n 0 gt + % DG/SR modification begin - Nov. 7, 1997 - Patch 1 + %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } + { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } + % DG/SR modification end + { 2 setlinecap } ifelse + /i y1 def + /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def + /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def + y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if + { newpath i dy mul dup x0 exch moveto + b 0 gt { gsave c i a cvs dup stringwidth pop + /z2 ED + w 0 gt {z1 z2 add neg} {z1} ifelse + h 0 gt {z1} {b neg} ifelse + rmoveto show grestore } if + dup f exch t moveto + g exch t L stroke + /i i h add def + } repeat + grestore +} def +% +/ArcArrow { + /d ED /b ED /a ED + gsave + newpath 0 -1000 moveto clip + newpath + 0 1 0 0 b + grestore + c mul + /e ED + pop pop pop r a e d PtoC y add exch x add + exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c + mul neg d +} def +% +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +% +/ArcAdjust { %%%% Vincent Guirardel +% given a target length (targetLength) and an initial angle (angle0) [in the stack], +% let M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0). +% This computes an angle t such that (x0,y0) is at distance +% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)). +% NOTE: this an absolute angle, it does not have to be added or substracted to angle0 +% contrary to TvZ's code. +% To achieve, this, one iterates the following process: start with some angle t, +% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]. +% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned. +% +% Another difference with TvZ's code is that we need d (=add/sub) to be defined. +% the value of d = add/sub is used to know on which side we have to move. +% It is only used in the initialisation of the angle before the iteration. +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input stack: 1: target length 2: initial angle +% variables used : rx, ry, d (=add/sub) +% + /targetLength ED /angle0 ED + /x0 rx angle0 cos mul def + /y0 ry angle0 sin mul def +% we are looking for an angle t such that (x0,y0) is at distance targetLength +% from the point M(t)=(rx*cos(t),ry*sin(t))) +%initialisation of angle (using 1st order approx = TvZ's code) + targetLength 57.2958 mul + angle0 sin rx mul dup mul + angle0 cos ry mul dup mul + add sqrt div +% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees +% (if the ellipse is very curved at the point where we draw the arrow, % +% the value can be much more than 360 degrees !) +% this should avoid going on the wrong side (more than 180 degrees) or go near +% a bad attractive point (at 180 degrees) + dup 90 ge { pop 90 } if + angle0 exch d % add or sub +% maximum number of times to iterate the iterative procedure: +% iterative procedure: takes an angle t on top of stack, computes a +% better angle (and put it on top of stack) + 30 { dup +% compute distance D between (x0,y0) and M(t) + dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt +% if D almost equals targetLength, we stop + dup targetLength sub abs 1e-5 le { pop exit } if +% stack now contains D t +% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]: +% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 ) + exch dup cos rx mul x0 sub exch sin ry mul y0 sub +% stack contains: y(t)-y0, x(t)-x0, d + 2 index Div targetLength mul y0 add ry Div exch + 2 index Div targetLength mul x0 add rx Div +% stack contains x(t')/rx , y(t')/ry , d +% now compute t', and remove D from stack + atan exch pop + } repeat +% we don't look at what happened... in particular, if targetLength is greater +% than the diameter of the ellipse... +% the final angle will be around /angle0 + 180. maybe we should treat this pathological case... +% after iteration, stack contains an angle t such that M(t) is the tail of the arrow +% to give back the result as a an angle relative to angle0 we could add the following line: +% angle0 sub 0 exch d +% +% begin bug fix 2006-01-11 +% we want to adjust the new angle t' by a multiple of 360 so that | t'-angle0 | <= 180 +%(we don't want to make the ellipse turn more or less than it should)... +dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse +% end bug fix +} def +% +/EllipticArcArrow { + /d ED % is add or sub + /b ED % arrow procedure + /a1 ED % angle + gsave + newpath + 0 -1000 moveto + clip % Set clippath far from arrow. + newpath + 0 1 0 0 b % Draw arrow to determine length. + grestore +% Length of arrow is on top of stack. Next 3 numbers are junk. +% + a1 exch ArcAdjust % Angular position of base of arrow. + /a2 ED + pop pop pop + a2 cos rx mul xOrig add % hv 2007-08-29 x->xOrig + a2 sin ry mul yOrig add % hv 2007-08-29 y->yOrig + a1 cos rx mul xOrig add % + a1 sin ry mul yOrig add % +% Now arrow tip coor and base coor are on stack. + b pop pop pop pop % Draw arrow, and discard coordinates. + a2 CLW 8 div +% change value of d (test it by looking if `` 1 1 d '' gives 2 or not ) + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse + ArcAdjust +% resets original value of d + 1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse % Adjust angle to give overlap. +} def +%%------------------ tvz/DG/hv (2004-05-10) end -------------------%% +% +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +% +/RotBegin { + tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if + /TMatrix [ TMatrix CM ] cvx def + /a ED + a Rot /RAngle [ RAngle dup a add ] cvx def +} def +% +/RotEnd { + /TMatrix [ TMatrix setmatrix ] cvx def + /RAngle [ RAngle pop ] cvx def +} def +% +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +% +/Uput { + /a ED + add 2 div /h ED 2 + div /w ED + /s a sin def + /c a cos def + /b s abs c abs 2 copy gt dup + /q ED + { pop } { exch pop } ifelse def + /w1 c b div w mul def + /h1 s b div h mul def + q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse +} def +% +/UUput { + /z ED + abs /y ED + /x ED + q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse + { x x mul y y mul sub z z mul add sqrt z add } + { q { x s div } { x c div } ifelse abs + } ifelse + a PtoC + h1 add exch + w1 add exch +} def +% +/BeginOL { + dup (all) eq exch TheOL eq or + { IfVisible not { Visible /IfVisible true def } if } + { IfVisible { Invisible /IfVisible false def } if } ifelse +} def +% +/InitOL { + /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def + /Visible { CP OLUnit idtransform T moveto } def + /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def + /BOL { BeginOL } def + /IfVisible true def +} def +% +end +%-----------------------------------------------------------------------------% +% +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-algparser.pro 0 0 +% $Id: pst-algparser.pro 26 2008-06-14 11:50:02Z herbert $ +%% +%% PostScript prologue for PSTricks algorithm parser +%% Version 0.01, 2008/01/01 +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%%-----------------------------------------------------------------------------% +% +/AlgParser { tx@AlgToPs begin AlgToPs end } def % Dominique Rodriguez +% +/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin +% +% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.12 +% E->T|E+T +% T->FS|T*FS +% FS -> F | +FS | -FS +% F->P|F^SF +% P->(E)|literal +% literal->number|var|var[E]|func(params) +% params->E|E,param +% number->TOBEFINISHED +% +%% E expression, T term, SF signed factor, F factor, P power +% +%% parser +% +%% str +% +%% C->EE +%% STR index -> STR index+lenExpr +/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp } def +% +%% analyze Expression List (separator , or | ) +%% STR index -> STR index+lenExpr +%% /AnalyzeListOfE { +%% { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar +%% NextNonBlankChar dup 0 eq { pop exit } if +%% dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if +%% pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop +%% AnalyzeListOfEPostHook +%% } def +/AnalyzeListOfE { + /NotFirst false def + { NextNonBlankChar pop AnalyzeExpr + NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse + dup Strlen eq { exit } if NextNonBlankChar + dup 44 ne 1 index 124 ne and + { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } + if pop 1 add } loop + AnalyzeListOfEPostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% E->T|E+T +%% STR index -> STR index+lenExpr +/AnalyzeExpr { + AnalyzePreHook AnalyzeTerm IsEndingExpr + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% T->FS|T*FS +%% STR index +/AnalyzeTerm { + AnalyzePreHook AnalyzeSignedFactor IsEndingTerm + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop } + ifelse + AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% FS -> F | +FS | -FS +%% STR index +/AnalyzeSignedFactor { + AnalyzePreHook 2 copy get dup IsUnaryOp + { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp } + { pop AnalyzeFactor } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% F->P|F^P +%% STR index +/AnalyzeFactor { + AnalyzePreHook AnalyzePower IsEndingFactor + { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse } + { { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower IsEndingFactor { pop exit } if} loop } + ifelse AnalyzePostHook +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% P->(E)|literal +%% STR index +/AnalyzePower { + %% depending of first char either a number, or a literal + 2 copy get dup 40 eq%%an open par + { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop } + { AnalyzeLiteral } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index STR[index] -> STR index +%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def +/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% recognize + or - +%% chr -> T/F +/IsUnaryOp { dup 43 eq exch 45 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadNumber { + exch dup 3 -1 roll dup 3 1 roll + %%read mantissa + { 1 add 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop + dup 101 eq exch 69 eq or + %%% there is a "e" or "E" -> read exponant + { 1 add 2 copy get dup IsUnaryOp + { pop 1 add 2 copy get } if + { IsNumber not { exit } if 1 add 2 copy get } loop } + if + dup 4 1 roll + 3 -1 roll exch 1 index sub getinterval +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a number can contain only : 0123456789. +%% chr -> T/F +/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index number +%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)? +%% STR index -> STR index' number +/ReadCondOp { + NextNonBlankChar 1 index 4 1 roll + { IsCondOp not { exit } if 1 add 2 copy get } loop + 2 copy 5 -1 roll + exch 1 index sub getinterval 3 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can contain only : 0123456789. +%% chr -> T/F +/IsLiteral {% + dup 48 ge exch dup 57 le 3 -1 roll and exch + dup 65 ge exch dup 90 le 3 -1 roll and 3 -1 roll or exch + dup 97 ge exch 122 le and or } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)? +%% STR index -> literal STR index' nextchr +/ReadLiteral { + exch dup 3 -1 roll dup 3 1 roll + %%read literal core + { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop + 4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a clpar +%% STR index -> STR index STR[index] T/F +/IsEndingExpr {% + 2 copy dup Strlen eq + %% if end of str is reached -> end ! + { pop pop 0 true } + %% ending chr -> clpar, comma, |, <, >, =, !, + {get dup dup 41 eq + exch dup 124 eq + exch dup 93 eq + exch dup 44 eq + exch dup 30 eq + exch dup 60 ge exch 62 le and or or or or or} + ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or a +- +%% STR index -> STR index STR[index] T/F +/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or */ +%% STR index -> STR index STR[index] T/F +/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% expr is ended by end of str or ^ +%% STR index -> STR index STR[index] T/F +/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% STR index -> STR index STR[index] +/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def +/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def +%%%%%%%%%%%%%%%%%%%%%%%% +%% DEBUG +/BRK {false} def +/BRKtrue {/BRK true def} def +/BRKStop {BRK {BRKtoto} if } def +/BRKEvalStop {BRK exch if } def +/BRKBRK2true {BRK {BRK2true} if } def +/BRK2 {false} def +/BRK2true {/BRK2 true def} def +/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def +end +% +%-------------------------------------------------------------------------------% +% +/tx@AlgToPs 12 dict def tx@AlgToPs begin +% +%% algExpr -> PSVector +/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def +/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def +/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def +/Strlen 0 def +/EvalListOfExpr {} def% +/EvalNumber {% + ReadNumber cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx + exch 1 add array astore def NextNonBlankChar pop } def +/EvalAddSub {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def +} def +/EvalMulDiv {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + 42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def +} def +/EvalPower {% + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll + pop /exp cvx exch 1 add array astore def +} def +/EvalLiteral {% + ReadLiteral + dup 40 eq%%% there is an open par -> function call + { pop 2 index + dup (Sum) eq { EvalSum } + { dup (IfTE) eq { EvalCond } + { dup (Derive) eq { pop EvalDerive } + { pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc + /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx + exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse } + { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def + dup 91 eq%%% there is an open bracket -> vector element + { pop 1 add NextNonBlankChar pop AnalyzeExpr + /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add } + { pop NextNonBlankChar pop } + ifelse} + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% the derive function : Derive(n,f(x)) +%% firstparindex lastparindex -> +/EvalDerive { + %% manage the function descripiton + 1 add ReadNumber 3 1 roll NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + 1 add NextNonBlankChar pop + 3 -1 roll cvi + dup 0 eq + { pop AnalyzeExpr 3 -1 roll pop 1 add } + { 1 sub 3 1 roll (x) exch tx@Derive begin DeriveIndexed end 4 -1 roll + { (x) tx@Derive begin Derive end } repeat + ExpressionVector exch /ExpressionVector [] def + AlgToPs aload length + /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll /l2 exch def /l1 exch def + l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add + 1 index length /Strlen exch def } ifelse +} def +/EvalSum {% + pop 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll + 5 -1 roll 4 add array astore def + %% keep ExpressionVector for later and create a new one for internal Sum computation + ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def + 1 add NextNonBlankChar pop AnalyzeExpr + %% add each term + /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def + /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add + array astore def 3 -1 roll pop 1 add +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +/EvalCond {% + pop 1 add AnalyzeCond NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + ExpressionVector 3 1 roll /ExpressionVector [] def + 1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def + NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add AnalyzeExpr + NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if + ExpressionVector + /ExpressionVector 6 -1 roll aload length dup + 6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def + 1 add 3 -1 roll pop +} def +%% CondOp STR index +/EvalCondOp {% + 3 -1 roll + dup (=) eq { /eq } {% + dup (<) eq { /lt } {% + dup (>) eq { /gt } {% + dup (>=) eq { /ge } {% + dup (<=) eq { /ge } {% + dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator } + ifelse } ifelse } ifelse } ifelse } ifelse } ifelse + cvx exch pop + /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def +/EvalUnaryOp { + 3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook {} bind def +/PreEvalHook {} bind def +/AnalyzeListOfEPostHook {} bind def +/AnalyzePostHook {} def +/RollOp { 3 1 roll } bind def +end %tx@CoreAnalyzerDict +% +%--------------------------------------------------------------------% +% +/tx@Derive 41 dict def tx@Derive begin +%%increase ^^ for each function added +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable -> PSVector +/Derive {% + 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end +} def +/Strlen 0 def +/InitParser { dup length /Strlen exch def 0 } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% algExpr variable index -> PSVector +/DeriveIndexed {% + 3 1 roll 10240 string 3 1 roll 0 3 1 roll + /Variable exch def + tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u,v)'=-(u',v') +/EvalListOfExpr {% + 4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe + 2 copy 7 -1 roll dup length 4 1 roll putinterval add + 6 -2 roll pop pop + 2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (-u)'=-(u') +/EvalUnaryOp { + 4 -2 roll 4 index (0) eq + { (0) StrConcat 7 -1 roll pop } + { 7 -1 roll 45 eq + { AddSub AddOpPar true } { false } ifelse + 3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + 7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (number)'=0 +/EvalNumber { ReadNumber (0) 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u+v)'=u'+v' +/EvalAddSub {% + 7 index dup (0) eq + { pop true }%% du=0 nothing added + { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false } + ifelse + 5 index dup (0) eq + { pop { (0) } { 4 -2 roll 2 copy pop 0 6 2 roll GetIntervalNewStr } ifelse }%%dv=0 + { exch + { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added + { 5 -2 roll 7 index 43 eq%%something yet added + { AddAdd false } { AddSub AddOpPar true } ifelse } + ifelse 11 1 roll + 3 -1 roll StrConcat 10 -1 roll { AddClPar } if + 2 copy pop 0 6 2 roll GetIntervalNewStr } + ifelse + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)' or (u/v)' +/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u*v)'=u'*v+u*v' +/EvalMul {% + 4 -2 roll 7 index dup (0) eq + { pop false }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if + true }%%du!=0 + ifelse + 5 1 roll 5 index (0) eq + { 5 -1 roll not { (0) StrConcat } if }%%dv=0 + { 5 -1 roll { AddAdd } if + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + }%%dv!=0 + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u/v)'=(u'*v-u*v')/v^2 +/EvalDiv {% + 4 -2 roll + 4 index (0) eq%%dv=0 -> u'/v + { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse } + { 7 index dup (0) eq + { pop }%%du=0 + { (1) eq%%du=1 + { false } + { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse + 3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0 + ifelse + AddSub + 4 index (1) eq + { 8 index StrConcat } + { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar } + ifelse + %}%%dv!=0 + 2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar + AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add } + ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str1 index str2 -> str1 index +/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def +/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u) +/EvalPower {% + 4 -2 roll 7 index (0) eq + {%%if du=0 then (u^v)'=v'ln(u)u^v + 4 index (0) eq + { (0) StrConcat }%%if dv=0 then (u^v)'=0 + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if + 8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if + AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse + } + {%%du!=0 + 4 index (0) eq + {%%if dv=0 then (u^v)'=vu'u^(v-1) + 5 index dup IsStrNumber + { dup (0) eq + { StrConcat } + { dup dup (1) eq exch (1.0) eq or + { StrConcat } + { StrConcat + 7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1 + { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006 + (*\() StrConcat 8 index StrConcat (\)) StrConcat + 5 index dup dup (2) eq exch (2.0) eq or + { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse } + { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)) StrConcat } ifelse + } + {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u) + 7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if + AddOpPar 5 index StrConcat (\)*\() StrConcat + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (-1\)+\() StrConcat + 4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if + 8 index StrConcat (\)^\() StrConcat + 5 index StrConcat (\)*ln\() StrConcat + 8 index StrConcat AddClPar + } ifelse + } ifelse + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% str -> true/false +/IsStrNumber {% + true exch + { dup 48 lt exch dup 57 gt 3 -1 roll or + exch dup 46 ne%%. + exch dup 43 ne%%+ + exch 45 ne%%- + and and and { pop false } if } forall +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalLiteral {% + ReadLiteral dup 40 eq%%% there is an open par -> function call + { pop (EvalFunc_ ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec } + { dup 91 eq%%% there is an open bracket -> vector element + { ERROR_vector_not_yet_implemented } + { pop EvalVariable } + ifelse } + ifelse +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% first last parpos Expr[first:parpos-1] -> +/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% (f(u))'=u'f'(u) +/EvalFunc { + 4 2 roll 4 index (1) ne + { AddOpPar 4 index StrConcat (\)*) StrConcat } if + (Eval ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Func derivative -> Eval +/EvalFunc_sin {% + PreCommonFunc + { (cos\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_cos {% + PreCommonFunc + { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_tan {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_asin {% + PreCommonFunc + { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_acos {% + PreCommonFunc + { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_atg {% + PreCommonFunc + { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_ln {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_exp {% + PreCommonFunc + { (exp\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_sqrt {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Fact {% + PreCommonFunc { ERROR_no_variable_expression_in_Fact } if + PostCommonFunc } def +/EvalFunc_sh {% + PreCommonFunc + { (ch\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_ch {% + PreCommonFunc + { (sh\() StrConcat 5 index StrConcat AddClPar } if + PostCommonFunc } def +/EvalFunc_th {% + PreCommonFunc + { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argsh {% + PreCommonFunc + { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argch {% + PreCommonFunc + { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if + PostCommonFunc } def +/EvalFunc_Argth {% + PreCommonFunc + { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if + PostCommonFunc } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +/PreCommonFunc { + 1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop + 4 2 roll 4 index (0) eq + { (0) StrConcat false } + { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse +} def +/PostCommonFunc { + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +/EvalFunc_Derive {% + 1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs + 4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add + 4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval + exch 6 2 roll } def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_Sum {% + 1 add NextNonBlankChar pop + %% read the variable name + ReadLiteral pop 3 -1 roll pop NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if + %% read the initial value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if + %% read the increment value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if + %% read the limit value + 1 add NextNonBlankChar pop ReadNumber pop + 2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if + 1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat + 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% literal switch -> func call, vector, variables +/EvalFunc_IfTE {% + 3 -1 roll pop 1 add NextNonBlankChar pop SkipCond + NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if + 1 add NextNonBlankChar pop dup 5 1 roll + AnalyzeExpr NextNonBlankChar + 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if + 1 add NextNonBlankChar pop + AnalyzeExpr 1 add NextNonBlankChar pop + 4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat + 6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar + 2 copy pop 0 6 2 roll GetIntervalNewStr + mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% advance in str until a comma is found (no error detection!) +%% str index -> str index' +/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Convert to radians if trigo function call +%% (name) -> +/TrigoFunc { + dup (cos) eq 1 index (sin) eq or exch (tan) eq or + { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add + array astore def + } if +} def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% No derivative for condition.... +/EvalCondOp { 3 -1 roll pop } bind def +/PutIntervalOneAdd {putinterval 1 add} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add close parenthesis in string at the given index +%% str index -> str index+1 +/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add 0 in string at the given index +%% str index -> str index+1 +/AddZero {2 copy (0) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddMul {2 copy (*) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add open parenthesis in string at the given index +%% str index -> str index+1 +/AddDiv {2 copy (/) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a plus sign in string at the given index +%% str index -> str index+1 +/AddAdd {2 copy (+) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a minus sign in string at the given index +%% str index -> str index+1 +/AddSub {2 copy (-) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Add a pipe sign in string at the given index +%% str index -> str index+1 +/AddPipe {2 copy (|) PutIntervalOneAdd} bind def +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% H O O K S +/AnalyzePreHook { dup 5 1 roll } bind def +/PreEvalHook {} def +/AnalyzePostHook { 7 -1 roll pop } bind def +/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def +/RollOp { 5 1 roll } bind def +end%%%tx@CoreAnalyzerDict +/tx@AddMathFunc 12 dict def tx@AddMathFunc begin +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% NEW FUNC +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2)) +%% x -> theta +/asin {% + dup abs 1 gt { EQDFasinrangeerror } if + dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad +} def +%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x) +%% x -> theta +/acos {% + dup abs 1 gt { EQDFacosrangeerror } if + dup dup mul 1 exch sub sqrt exch atan DegtoRad +} def +%% function arctangent in radians +%% x -> theta +/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def +%% HYPERBOLIC FUNCTIONS +/sh { dup Ex exch neg Ex sub 2 div } def +/ch { dup Ex exch neg Ex add 2 div } def +/th { dup sh exch ch div } def +/Argsh { dup dup mul 1 add sqrt add ln } def +/Argch { dup dup mul 1 sub sqrt add ln } def +/Argth { dup 1 add exch 1 exch sub div ln 2 div } def +%% modified exponential funtion for 0 +%% x n -> x^n +/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def +%% modified exponential funtion for 0 +%% x -> e^x +/Ex { Euler exch exp } bind def +%% +%% factorial function +%% n -> n! +/Fact { 1 exch 2 exch 1 exch { mul } for } bind def +/fact { Fact } bind def +end + +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +% $Id: pst-dots.pro 26 2008-06-14 11:50:02Z herbert $ +% +%% PostScript prologue for pstricks.tex. +%% Version 2.02, 2008/04/18 +%% +%% For distribution, see pstricks.tex. +%% +%% Timothy Van Zandt +%% +%% This program can be redistributed and/or modified under the terms +%% of the LaTeX Project Public License Distributed from CTAN archives +%% in directory macros/latex/base/lppl.txt. +%% +%% Modified by Etienne Riga - Dec. 16, 1999 +%% Modified by Etienne Riga - 2005/01/01 (er) +%% to add /Diamond, /SolidDiamond and /BoldDiamond +%% Modified by Herbert Voss (hv) - 2008/04/17 +% +10 dict dup begin % hold local + /FontType 3 def + /FontMatrix [.001 0 0 .001 0 0] def + /FontBBox [-571.5 -742.5 571.5 742.5] def +% /FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph + /Encoding 256 array def + 0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef + Encoding % replace with given dot names + dup (b) 0 get /Bullet put % get the numerical position of b in ASCII +% % and save /Bullet at this place in Encoding + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put % 67 + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +%%% + dup (k) 0 get /Asterisk put + dup (K) 0 get /BoldAsterisk put + dup (J) 0 get /SolidAsterisk put + dup (h) 0 get /Hexagon put + dup (H) 0 get /BoldHexagon put + dup (G) 0 get /SolidHexagon put + dup (f) 0 get /Octogon put % 2008-04-18 hv + dup (F) 0 get /BoldOctogon put % 2008-04-18 hv + dup (g) 0 get /SolidOctogon put % 2008-04-18 hv + dup (a) 0 get /Add put + dup (A) 0 get /BoldAdd put % 65 + dup (x) 0 get /Mul put + dup (X) 0 get /BoldMul put + dup (m) 0 get /Oplus put + dup (M) 0 get /BOplus put + dup (e) 0 get /SolidOplus put + dup (n) 0 get /Otimes put + dup (N) 0 get /BOtimes put + dup (E) 0 get /SolidOtimes put + dup (i) 0 get /Bar put + dup (I) 0 get /BoldBar put + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +%%% +/CharProcs 47 dict def +CharProcs begin + /CirclePath {0 0 500 0 360 arc closepath} def + /Bullet {CirclePath fill} def + /Circle {CirclePath .9 .9 scale CirclePath eofill} def + /BoldCircle 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476 -275 lineto 476 275 lineto closepath + } def + /SolidHexagon {HexagonPath fill} def + /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def + /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def +% 2008-04-18 hv + /OctogonPath { + 550 dup 22.5 tan mul dup neg dup add /xMove exch def + exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def + /SolidOctogon { OctogonPath fill } def + /Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def + /BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def +% + /AsteriskPath { + 20 0 moveto 10 250 180 500 0 500 curveto + -180 500 -10 250 -20 0 curveto closepath + } def + /Asterisk { + AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath + 60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill + } def +% + /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def + /BoldAsteriskPath { + 50 30 cos 100 mul moveto Basterp + 60 rotate Basterp 60 rotate 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+\title[$\Ptau \to \Pmu \Pmu \Pmu$ approval presentation ]{$\Ptau \to \Pmu \Pmu \Pmu$ approval presentation} + + \author[Paul Seyfert]{ + Johannes Albrecht\inst{1}, Marta Calvi\inst{2}, \underline{Marcin Chrzaszcz\inst{3,4}}, \\Laura Gavardi\inst{1}, Jon Harrison\inst{5}, Basem Khanji\inst{2}, George Lafferty\inst{5}, Tatiana Likhomanenko\inst{6}, Eduardo Rodrigues\inst{5}, \\Nicola Serra\inst{3}, Paul Seyfert\inst{7}\\{~}\\ +\textbf{Referees}:\\ Benoit Viaud (Chair) , Matteo Rama, Frederic Machefert (EB) } + \institute[Uni Heidelberg]{ + \inst{1}Dortmund, + \inst{2}Milano Bicocca, + \inst{3}Zurich, \inst{4}IFJ Cracow, \inst{5}Manchester, \inst{6}Yandex, \inst{7}Uni. Heidelberg + } +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin Chrz\k{a}szcz} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ)} + + + % \begin{frame}\frametitle{Outline} + % \begin{enumerate} + % \item introduction\vspace{.5em} + % \item multivariate technique\vspace{.5em} + % \item normalisation\vspace{.5em} + % % \item backgrounds\vspace{.5em} + % \item expected sensitivity\vspace{.5em} + % \item model dependence\vspace{.5em} data from Reco14Stripping20(r1) + % \end{enumerate} + % Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green} + % \end{frame} + + \begin{frame}\frametitle{Outline} + \tableofcontents + \end{frame} + + + + + \begin{frame} + \frametitle{Yellow pages} + \begin{itemize} + \item TWiki: \href{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}{\url{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}} + \item ANA note: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/v8.pdf}{LHCb-ANA-2014-005} + \item Paper draft: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/paper_v1.pdf}{LHCb-PAPER-2014-X} + \item Target journal: JHEP + \item Conference: Tau 2014 + \end{itemize} + + \end{frame} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Introduction} + + \begin{frame} + \frametitle{Status of $\Ptau\to\Pmu\Pmu\Pmu$} + \begin{columns} + \begin{column}{.62\textwidth} + + \includegraphics[width=.95\textwidth]{feymn.png} + + {{ + \begin{itemize} + \item Charged Lepton Flavour Violation process + \item Possible as penguin with neutrino oscillation + \item SM prediction is beyond experimental reach~$O(10^{-40})$ + + \end{itemize} + }} + \end{column} + \begin{column}{.45\textwidth} + \begin{alertblock}{current limits ($ 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{alertblock} + \begin{alertblock}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \item[and many more...] + \end{description} + \end{alertblock} + \end{column} + \end{columns} + \end{frame} +%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item Following same approach as other RD searches. + \item Loose stripping selection + \item Multivariate classification in: mass, PID, ``geometry/topology'' + \item Binning optimisation. + \item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$) + \item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$ + \item ``middle sidebands'' for classifier evaluation and tests.($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$). + \item CLs for limit calculation + \end{itemize} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \begin{frame} + \frametitle{$\Ptau$ production} + \begin{itemize} + \item Consider five production channels (fractions at $\unit{8}{\TeV}$):\begin{itemize} + \item Prompt $\PDs\to\Ptau$ ($72.4\pm2.7\,\%$) + \item Prompt $\PDplus\to\Ptau$ ($4.2\pm0.7\,\%$) + \item Non-prompt $\PDs\to\Ptau$ ($8.5\pm1.7\,\%$) + \item Non-prompt $\PDplus\to\Ptau$ ($0.17\pm0.04\,\%$) + \item $X_{\Pbottom}\to\Ptau$ (meson or baryon) ($14.7\pm2.3\,\%$) + \end{itemize} + \item Use $\sigma(\Pbottom\APbottom)$ at $\unit{8}{\TeV}$ from LHCb + \item Use Pythia scaling for $\sigma(\Pcharm\APcharm)$ at $\unit{8}{\TeV}$ + \end{itemize} + + \begin{columns} + \column{0.8\textwidth} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$ + \item One can calculate it form: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space + \item \texttt{hep-ex:0604043} + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=1.0\times10^{-3}$ + \end{itemize} + \end{exampleblock} + \column{0.2\textwidth} + {~} + \end{columns} + + \end{frame} + \begin{frame} + \frametitle{Datasets} + \begin{itemize} + \item Data from Reco14Stripping20(r1) + \item Much MC\begin{itemize} + \item 24M Inclusive background events ($\Pbottom\APbottom$ and $\Pcharm\APcharm$) + \item 10M Exclusive background events ($\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$) + \item 2M Signal events (split over 5 production channels) + \item 12M $\PD \to \PK \Ppi \Ppi$ (missID studies) + \item 10M $\PDstar \to \PD(\PK \Pmu \Pnum) \Ppi$ (missID studies) + + \end{itemize} + \item[$\Rightarrow$] Generator level cuts for improved use of computing resources + \begin{itemize} + \item $\sim 14$ times more signal statistics after stripping + \item $\sim 2$ times more background statistics + \end{itemize} + \item Mix $\Ptau$ production on ntuple level instead of reweighting. + \newline$\Rightarrow$ Ease up ntuple usage (no forgotten weighting, no double weighting, \dots) + \end{itemize} + \end{frame} + \section{Selection} + \begin{frame} + \frametitle{Stripping and selection} +{\footnotesize{ +\begin{tabular}{|c|cc|} +\hline + &$\Ptau\to\Pmu\Pmu\Pmu$&$\PDs\to\Pphi\Ppi$\\ +\hline +$\mu^\pm$ , $ \pi^\pm$ &\multicolumn{2}{c|}{} \\ +$p_T$ &\multicolumn{2}{c|}{$>300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +track ghost probability &\multicolumn{2}{c|}{$<0.3 $} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +IP $\chi^2$ &\multicolumn{2}{c|}{$<225 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + + \end{frame} + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + \begin{frame} + \frametitle{Triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & $||$ Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{$^1$ triggers in 2012} + \begin{itemize} + \item Cuts changed through 2012 + \item[$\rightarrow$]emulated two different TCKs for 2012 + \item[$\rightarrow$] Found negligible differences + \item Choice of triggers were optimised based on $\dfrac{s}{\sqrt{b}}$ FOM. + \end{itemize} + \end{block}} + % \only<2>{ + % \begin{block}{$^2$ word on Hlt2DiMuonDetached} + % \begin{itemize} + % \item keep it simple here + % \item line unchanged in 2012 + % \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + % \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + % \end{itemize} + % \end{block}} + + \end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \section{Multivariate technique} + + \begin{frame} + \frametitle{Geometric likelihood} +Much work has been put in improving our geometric and kinematic classifier: + \begin{itemize} + \item Classify the displaced 3-body decay properties of a signal candidate + \item Revisit variable choice + \item Revisit classification technique + \item More toolkits tried: MatrixNet, NeuroBayes, TMVA + \item Retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ BDT isolation: CERN-THESIS-2013-259) + \item Blending technique. + \end{itemize} + + \end{frame} + + \begin{frame} + \frametitle{Basic Setup - Step I} + \begin{itemize} + \item Train $1/3$ signal MC against $1/2$ background MC + \item variables \begin{itemize} + \item DOCA + \item Vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item Cone isolation + \item BDT isolation + \end{itemize} + \item Using these variables, train several classifiers (''Base'') \\for each of the $\Ptau$ source + \end{itemize} + \end{frame} + + + \begin{frame} + \frametitle{Step II} +\begin{itemize} +\item Train using second $1/3$ signal MC against second $1/2$ background MC. +\item Introduce Blending technique +\end{itemize} + \begin{exampleblock}{Blending technique} + \begin{itemize} + \item For each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, one LD classifier and MatrixNet classifier. + \item One final MatrixNet classifier using the 13 base variables and the base classifiers as input + + \end{itemize} + \end{exampleblock} + \begin{itemize} +\item All evaluation is done on $3rd$ $1/3$ signal sample and middle side-bands. +\item Splitting into independent samples makes the procedure insensitive to +overtraining. +\end{itemize} + + + \end{frame} + + + + \begin{frame} + \frametitle{Performance of Blend classifier} + \begin{itemize} + \item Classifier prefers $\Ptau$ from prompt $\PDs$ + \end{itemize} + \begin{columns} + \begin{column}{.48\textwidth} + \begin{exampleblock}{MC response for different\newline $\Ptau$ production channels} + \includegraphics[width=.95\textwidth]{./mn_sig.png} + \end{exampleblock} + \end{column} + \begin{column}{.48\textwidth} + \begin{exampleblock}{response for $\PDs\to\Pphi\Ppi$\newline data and MC} + \includegraphics[width=.95\textwidth]{./MN_BLEND_FLAT.png} + \end{exampleblock} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Calibration} + \begin{itemize} + \item Assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time) + \item Get correction $\PDs\leadsto\Ptau$ from MC + \item Apply corrections to $\PDs\to\Pphi\Ppi$ on data + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC + % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{MN_BLEND_FLAT.png} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item We used ProbNNmu already in the previous round of the analysis + \item Now use MC12TuneV2 (latest) + \item Two-fold reason:\begin{itemize} + \item Expect better performance than CombDLL variables + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$) + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{PID calibration } + \begin{itemize} + \item Since PIDCalib tool didn't work for us, we choose a phenomenological approach. + \item Many thanks to Barbara Sciascia for help understanding this problem. + \end{itemize} + \begin{exampleblock}{phenomenologic treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$ + \end{itemize} + \end{exampleblock} +\begin{itemize} +\item Many x-checks done. +\item Everything works fine. +\end{itemize} + + \end{frame} + + + + \begin{frame} + \frametitle{Binning optimisation} + \begin{itemize} + \item How to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$ + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier + \item Now: optimise two-dimensions (optimise bin boundaries in both dimensions at the same time) + \item Unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain) + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{Impact of new binning optimisation} + \begin{itemize} + \item Removal of tiny bins which contribute negligible sensitivity + \item Colour: limit obtained, using only this particular bin + \item Number: rank of that bin (1=best sensitivity bin) + \end{itemize} + + ~ + + \begin{columns} + \begin{column}{.5\textwidth} + old analysis + + ~ + + \includegraphics[width=.95\textwidth]{./90CLonebinlimit.pdf} + \end{column} + \begin{column}{.5\textwidth} + new analysis + + (2011 data) + \includegraphics[width=.95\textwidth]{./rank.pdf} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{Mass shape} + \begin{itemize} + \item Double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian) + \item Fix fraction to ease calibration:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + Calibrated $\Ptau$ Mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + + + + \section{Normalisation} + + \begin{frame} + \frametitle{Relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012 + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{Normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} (\%) & 8.989 \pm 0.40 & 9.21 \pm 0.35\\ +\hline +\rm{\epsilon_{cal}}^{GEN} (\%) & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} (\%) & 9.927 \pm 0.028 & 9.261 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} (\%) & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\phi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\tau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.89 \pm 0.12 & 1.96 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} (\%) & 35.52 \pm 0.14 \pm 0.14 & 39.3 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} (\%) & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(PDs \to \Pphi \Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\tau}_{D_{s}} & 0.78 \pm 0.04 & 0.80 \pm 0.03 \\ +\hline +\mathcal{B} (\PDs \to \Ptau \Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.898 \pm 0.060 & 0.912 \pm 0.054 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6593 \pm 0.0058 & 0.525 \pm 0.040\\ +\hline +N_{cal} & 28,207 \pm 440 & 52,131 \pm 695\\ +\hline & \\[-0.8em]\hline +\alpha & (3.81 \pm 0.46) \times 10^{-9} & (1.72 \pm 0.23) \times 10^{-9}\\ +\alpha^{trash} & (7.20 \pm 0.98) \times 10^{-9} & (3.37 \pm 0.50) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{Backgrounds} + + \begin{frame} + \frametitle{Misidentification} + \begin{itemize} + \item Most dominant: $\PDplus\to\PK\Ppi\Ppi$ + \item Experience from last round: cut away low ProbNNmu range + \item Check remaining data under $\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \item $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$ start to become visible in 2012 + \end{itemize} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{Evil backgrounds} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy + \begin{itemize} + \item Modelled in CONF note + \item Optimised veto in PAPER + \item Right now: both versions in the ANA note + \end{itemize} + \item Baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$ + \begin{itemize} + \item Fits better understood + \item Sensitivity unchanged when removing veto + \item Smaller uncertainty on expected background + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{Remaining backgrounds} + \begin{itemize} + \item Fit exponential to invariant mass spectrum in each likelihood bin + \item Don't use $\pm \unit{30}{\MeV}$ in the fit + \item[$\rightarrow$] Compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier developement} + \end{itemize} + {\begin{center} + Example of most sensitive regions in 2011 and 2012 + \includegraphics[width=0.9\textwidth]{./fits.png} + + \end{center}} + \end{frame} + + \section{Expected limit} + + \begin{frame} + \frametitle{expected limit} + \begin{itemize} + \item Consider nuisance parameters from background fit, signal pdf calibration, normalisation + \item Nuisance parameters due to $\Ptau$ production, normalization. + \item Limit for combined 2011+2012 analysis + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{Sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.0 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{./banana.png} + \end{frame} + + + + \section{Model dependence} + + \begin{frame} + \frametitle{Model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not applicable to New Physics with small $m_{\APmuon\Pmuon}$ + \item Model description in \texttt{arXiv:0707.0988} + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms + \end{itemize} + \only<2->{ + \begin{itemize} + \item With radiative distribution limit gets worse by $51\,\%$ (dominantly from the $\Peta$ veto) + \item The other four Dalitz distributions behave nicely (within $7\,\%$) + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.pdf} + \includegraphics[width=.331\textwidth]{./gammallrr.pdf} + \includegraphics[width=.331\textwidth]{./gammarad.pdf} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.pdf} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.pdf} +} + + \end{frame} + + + % \begin{frame} + % \frametitle{Conclusion} + % \begin{columns} + % \begin{column}{.55\textwidth} + % \begin{itemize} + % \item finally all pieces put together + % \item model (in)dependence of $\Peta$ veto investigated + % \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + % \end{itemize} + % \end{column} + % \begin{column}{.45\textwidth} + % \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + % \end{column} + % \end{columns} + + % \end{frame} + + + \section{Unblinded results} + + \begin{frame} + \frametitle{Unblinding 1} +\begin{columns} +\column{1in}{~} +\column{3in} +'' +THERE came a day at summer’s full \\ +Entirely for us \\ +I thought that such were for the saints, \\ +Where revelations be. ''\footnote{E.Dickinson} \\ + \column{1in}{~} +\end{columns} +{~}\\ +{~}\\ +\begin{Large} +On Monday $4^{th}$ of August we were given the permission to unblind. +\end{Large} + + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 2} +\begin{itemize} +\item Unfortunately no big ''revelations'' were there: +\item 2011 numbers: +\end{itemize} + \includegraphics[width=1.\textwidth]{2011.png} + + \end{frame} + + \begin{frame} + \frametitle{Unblinding 3} +\begin{itemize} +\item Unfortunately no big ''revelations'' were also in 2012 data: + +\end{itemize} + \includegraphics[width=1.1\textwidth]{2012.png} + + \end{frame} + + + + \begin{frame} + \frametitle{Unblinding 4} + + \begin{center} + \includegraphics[width=0.7\textwidth]{banana_line.pdf} + \end{center} +\begin{columns} + +\column{0.2in}{~} +\column{2in} +Limits(PHSP):\\ +Observed(Expected)\\ +$4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\ +$5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\ + + \column{3in} + \includegraphics[width=0.5\textwidth]{model.png} +\end{columns} + \end{frame} + + \begin{frame} + \frametitle{Conclusions} + \begin{columns} + \column{2.5in} + \begin{itemize} + \item We didn't find NP (yet). + \item Limits set with full LHCb dataset. + \item Awaiting for the future data! + \end{itemize} +\column{2.5in} + + \includegraphics[width=1\textwidth]{TauLFV_UL_2013001.pdf} + + + + \end{columns} + \begin{itemize} + \item We would like to thank our referees for very friendly,thorough and fruitful review. + \item With this presentation we ask collaboration for approval. + \end{itemize} + + + \end{frame} + + + +\end{document} diff --git a/tau23mu_lhcb/09_10_2014/mchrzasz2.aux b/tau23mu_lhcb/09_10_2014/mchrzasz2.aux new file mode 100644 index 0000000..3c3451e --- /dev/null +++ b/tau23mu_lhcb/09_10_2014/mchrzasz2.aux @@ -0,0 +1,28 @@ +\relax +\ifx\hyper@anchor\@undefined +\global \let \oldcontentsline\contentsline +\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} +\global 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+\usepackage{polski} +%\usepackage{amssymb,amsmath} +%\usepackage[latin1]{inputenc} +%\usepackage{amsmath} +%\newcommand\abs[1]{\left|#1\right|} +\usepackage{amsmath} +\newcommand\abs[1]{\left|#1\right|} +\usepackage{hepnicenames} +\usepackage{hepunits} +\usepackage{color} +\usepackage{feynmp} +\usepackage{pst-pdf} +\usepackage{hyperref} +\usepackage{xcolor} + +\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5 +\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25} + + +\usetheme{Sybila} +\title[ Quo Vadis $\color{white} \tau \to \mu \mu \mu$]{Quo Vadis $\color{white} \tau \to \mu \mu \mu$} + + \author[Marcin, Jon, George ]{Marcin, Jon, George + } + \institute[UZH, IFJ]{\begin{tiny} + + + \end{tiny} + } +\date{\today} +\begin{document} +% --------------------------- SLIDE -------------------------------------------- +\frame[plain]{\titlepage} +\author{Marcin, Jon, George} +% ------------------------------------------------------------------------------ +% --------------------------- SLIDE -------------------------------------------- + +\institute{~(UZH, IFJ, ManUni)} + + + % \begin{frame}\frametitle{Outline} + % \begin{enumerate} + % \item introduction\vspace{.5em} + % \item multivariate technique\vspace{.5em} + % \item normalisation\vspace{.5em} + % % \item backgrounds\vspace{.5em} + % \item expected sensitivity\vspace{.5em} + % \item model dependence\vspace{.5em} data from Reco14Stripping20(r1) + % \end{enumerate} + % Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green} + % \end{frame} + + + + + \begin{frame} + \frametitle{Things we discussed in Aachen} + \begin{itemize} +\item Next update should be with additional $5\invfb$ +\begin{itemize} +\item From emails it looks like Tim wants this as well. +\item Will be on top of Belle result. +\end{itemize} +\item Till then: +\begin{itemize} +\item We can play with the data we have to find improvements. +\item Try doing other $\Ptau$ decays. +\item We won't beat for sure B factories. +\end{itemize} +\item Thing to look at: +\begin{itemize} +\item $\tau \to \mu \mu e$ +\item $\tau \to \mu \mu \Pproton$ +\end{itemize} +\item Start with $\tau \to \mu \mu e$ and see how it goes. + \end{itemize} + + \end{frame} + + + + + + +\end{document} diff --git a/tau23mu_lhcb/09_10_2014/mchrzasz2.toc b/tau23mu_lhcb/09_10_2014/mchrzasz2.toc new file mode 100644 index 0000000..495658f --- /dev/null +++ b/tau23mu_lhcb/09_10_2014/mchrzasz2.toc @@ -0,0 +1,2 @@ +\beamer@endinputifotherversion {3.10pt} +\select@language {english} diff --git a/tau23mu_lhcb/09_10_2014/mixing.pdf b/tau23mu_lhcb/09_10_2014/mixing.pdf new file mode 100644 index 0000000..5cd0ea2 --- /dev/null +++ b/tau23mu_lhcb/09_10_2014/mixing.pdf Binary files differ diff --git a/tau23mu_lhcb/09_10_2014/mn_sig.png b/tau23mu_lhcb/09_10_2014/mn_sig.png new file mode 100644 index 0000000..784cef3 --- /dev/null +++ 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Likhomanenko\inst{6}, Eduardo Rodrigues\inst{5}, Nicola Serra\inst{4}, \underline{Paul Seyfert\inst{7}}} + + \institute[Uni Heidelberg]{ + \inst{1}Dortmund, + \inst{2}Milano Bicocca, + \inst{3}Cracow, \inst{4}Zurich, \inst{5}Manchester, \inst{6}Yandex, \inst{7}Heidelberg University + } + + \date{\today} + \subject{} + + + \AtBeginSection[] + { + \begin{frame}{} + \tableofcontents[currentsection,currentsubsection] + \end{frame} + } + + + \begin{document} + \begin{frame} + \titlepage + \end{frame} + + + \begin{frame} + \begin{enumerate} + \item introduction\vspace{.5em} + \item multivariate technique\vspace{.5em} + \item choice of triggers\vspace{.5em} + \item normalisation\vspace{.5em} + \item backgrounds\vspace{.5em} + \item expected sensitivity\vspace{.5em} + \item model dependence\vspace{.5em} + \end{enumerate} + Major news wrt.\ the previous analysis rounds highlighted in \textcolor{darkgreen}{green} + \end{frame} + + \section{introduction} + + \begin{frame} + \frametitle{Status $\Ptau\to\Pmu\Pmu\Pmu$} + \begin{columns} + \begin{column}{.62\textwidth} + \begin{fmffile}{sm} + \begin{fmfgraph*}(200,150) + \fmfstraight + \fmfleft{is3,is2,is1,i1,i2,i3,i4,i5,i6} + \fmfright{os3,os2,os1,o1,o2,o3,o4,o5,o6} + + + \fmf{phantom}{o1,g1} + \fmf{phantom,tension=1.5}{g1,i1} + + \fmffreeze + + \fmf{photon, tension=2.,lab.side=left, lab=$\Pphoton$}{g1,g2} + \fmf{fermion,lab.side=left,label=$\APmuon$}{o3,g2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{g2,o5} + \fmf{phantom,tension=1.5}{i6,g2} + + \fmffreeze + + + \fmf{fermion,lab.side=left,label=$\Pgtm$}{i1,w1} + \fmf{dashes,lab.side=right,label=$\PWminus$}{w1,w2} + \fmf{fermion,lab.side=left,label=$\Pmuon$}{w2,o1} + + + \fmfipath{p[]} + \fmf{plain,tension=0,right,label={$\Pgngt\to\Pgngm$},tag=1}{w1,w2} + \fmffreeze + \fmfiset{p1}{vpath1(__w1,__w2)} + \fmfiv{d.sh=cross,d.ang=0,d.size=5thick}{point length(p1)/2 of p1} + + + \end{fmfgraph*} + + \end{fmffile} + {\footnotesize{ + \begin{itemize} + \item charged Lepton Flavour Violation process + \item possible as penguin with neutrino oscillation + \item unmeasurable small + \end{itemize} + }} + \end{column} + \begin{column}{.37\textwidth} + \begin{block}{current limits ($ 90\,\%$ CL)} + + \begin{description} + \item[BaBar] $3.3\times 10^{-8}$ + \item[Belle] $2.1\times 10^{-8}$ + \item[LHCb] $8.0\times 10^{-8}$ + \end{description} + \end{block} + \begin{block}{BSM predictions} + \begin{description} + \item[var.\ SUSY] $10^{-10}$ + \item[non universal $\PZprime$] $10^{-8}$ + \item[mSUGRA+seesaw] $10^{-9}$ + \end{description} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{$\Ptau$ production} + \begin{itemize} + \item consider five production channels (fractions at $\unit{8}{\TeV}$):\begin{itemize} + \item prompt $\PDs\to\Ptau$ ($73.1\pm3.9\,\%$) + \item prompt $\PDplus\to\Ptau$ ($0.42\pm0.43\,\%$) + \item non-prompt $\PDs\to\Ptau$ ($9.7\pm2.1\,\%$) + \item non-prompt $\PDplus\to\Ptau$ ($0.02\pm0.02\,\%$) + \item $X_{\Pbottom}\to\Ptau$ (meson or baryon) ($16.8\pm3.0\,\%$) + \end{itemize} + \item \textcolor{darkgreen}{use $\sigma(\Pbottom\APbottom)$ at $\unit{8}{\TeV}$ from LHCb} + \item \textcolor{darkgreen}{use Pythia scaling for $\sigma(\Pcharm\APcharm)$ at $\unit{8}{\TeV}$} + \end{itemize} + \begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$} + \begin{itemize} + \item old analysis: used upper limit + \item now: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space + \item \texttt{hep-ex:0604043} + \item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=1\pm1\times10^{-4}$ + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{Strategy} + \begin{itemize} + \item mostly as in many rare decay searches: + \item loose stripping selection + \item multivariate classification in: mass, PID, ``geometry/topology'' + \item relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$) + \item invariant mass fit for expected background in each likelihood bin\newline fit in $m-m_{\Ptau}>\unit{30}{\MeV}$ + \item ``middle sidebands'' for classifier evaluation ($\unit{20}{\MeV}300\MeV$} \\ +Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\ +IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\ +\textcolor{darkgreen}{track ghost probability} &\multicolumn{2}{c|}{\textcolor{darkgreen}{$<0.3 $}} \\ +\hline +$\mu$ pairs &\multicolumn{2}{c|}{} \\ +$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\ +$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\ +$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\ +\hline +$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\ +$\Delta m$ & $<400\MeV$ & $<50\MeV$\\ +Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\ +\textcolor{darkgreen}{IP $\chi^2$} &\multicolumn{2}{c|}{$<225^1 $} \\ +$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\ +$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\ + &\multicolumn{2}{c|}{no PV refitting}\\ +decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\ + &\multicolumn{2}{c|}{PV refitting}\\ +\hline +\end{tabular} +}} + +{\footnotesize{$^1$ different LoKi functor}} + \end{frame} + + \section{multivariate technique} + + \begin{frame} + \frametitle{``geometric likelihood''} + \begin{itemize} + \item classify the displaced 3-body decay properties of a signal candidate + \item revisit variable choice + \item revisit classification technique + \item \textcolor{darkgreen}{more toolkits tried: MatrixNet, NeuroBayes}, TMVA + \item \textcolor{darkgreen}{retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ Laura's BDT isolation: CERN-THESIS-2013-259)} + \end{itemize} + + \end{frame} + \begin{frame} + \frametitle{setup} + \begin{itemize} + \item train $1/3$ signal MC against $1/2$ background MC + \item variables \begin{itemize} + \item $3\times$ DOCA + \item vertex $\chi^2$ + \item $\tau$ decay time + \item $\tau$ IP$\chi^2$ + \item min.\ $\mu$ IP$\chi^2$ + \item $\Ptau$ pointing angle + \item $\tau$ $p_T$ + \item max.\ track $\chi^2$ + \item $\PBs\to\Pmu\Pmu$ track isolation + \item cone isolation + \item \textcolor{darkgreen}{BDT isolation} + \end{itemize} + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{futher tweaking} + \begin{itemize} + \item \textcolor{darkgreen}{remove fully reconstructed 3-body decays from background sample\newline (don't expect to be able to discriminate these)} + \item don't apply trigger prior to training + \end{itemize} + + \begin{exampleblock}{``blending'' technique} + \begin{itemize} + \item for each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, and one LD classifier + \item[$\Rightarrow$] 50 classifiers + \item one final MatrixNet classifier using the 13 base variables and the 50 classifiers as input + \newline(trained on the second $1/3$ of signal MC and the second $1/2$ of background MC) + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{performance} + \begin{itemize} + \item classifier prefers $\Ptau$ from prompt $\PDs$ + \end{itemize} + \begin{columns} + \begin{column}{.48\textwidth} + \begin{block}{MC response for different\newline $\Ptau$ production channels} + \includegraphics[width=.95\textwidth]{./for_paul.png} + \end{block} + \end{column} + \begin{column}{.48\textwidth} + \begin{block}{response for $\PDs\to\Pphi\Ppi$\newline data and MC} + \includegraphics[width=.95\textwidth]{./MN_BLEND_FLAT.png} + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{calibration} + \begin{itemize} + \item assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time) + \item get correction $\PDs\leadsto\Ptau$ from MC + \item apply corrections to $\PDs\to\Pphi\Ppi$ on data + \end{itemize} + \begin{block}{validation} + \begin{itemize} + \item done for 2011 analysis, treating smeared MC as data + \end{itemize} + \end{block} + \begin{columns} + \begin{column}{.45\textwidth} + \begin{itemize} + \item $\PDs\to\Pphi\Ppi$ well modelled in MC + \item until the very low likelihood end of the distribution + \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=.95\textwidth]{MN_BLEND_FLAT.png} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{PID} + \begin{itemize} + \item we used ProbNNmu already in the previous round of the analysis + \item now use MC12TuneV2 (latest) + \item two-fold reason:\begin{itemize} + \item expect better performance than CombDLL variables + \item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$) + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{PIDCalib} + \begin{itemize} + \item calibration strategy: use PIDCalib + \item confirm with $\PDs\to\Pphi\Ppi$ if everything is fine + \end{itemize} + \begin{columns} + \begin{column}{.45\textwidth} + cut\&fit: + \begin{itemize} + \item fit $\PDs\to\Pphi\Ppi$ with a TIS muon in data + \item cut on ProbNNmu of one muon + \item fit again + \item[$\rightarrow$] ratio is ``true'' cut efficiency + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=86.3\,\%$ + \end{block} + \end{column} + \begin{column}{.45\textwidth} + PIDCalib + \begin{itemize} + \item apply full selection (incl. trigger) to $\PDs\to\Pphi\Ppi$ MC reference sample + \item avoid IsMuon bias + \end{itemize} + \begin{block}{ProbNNmu>0.4} + $\varepsilon=89.8\,\%$ + \end{block} + \end{column} + \end{columns} + \end{frame} + + \begin{frame} + \frametitle{?} + \begin{itemize} + \item first shown at \myhref{https://indico.cern.ch/event/291727/}{charming VRD meeting} + \item also mentionned at last \myhref{https://indico.cern.ch/event/298021/}{LHCb week} + \item many emails exchanged with Barbara Sciascia + \item mistakes on user side found + \item still no agreement + \end{itemize} + \begin{exampleblock}{phenomenologic treatment} + \begin{itemize} + \item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC + \newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$ + \item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$ + \item assign error of $0.02$ for $c$ + \end{itemize} + \end{exampleblock} + \begin{itemize} + \item planned: investigate further (usage/bug/samples) + \item planned: use muons from $\PDs\to\Pphi\Ppi$ directly + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{binning optimisation} + \begin{itemize} + \item how to optimise the binning in two classifiers? + \item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$ + \item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier + \item \textcolor{darkgreen}{now: optimise two-dimensions (optimise bin boundaries in both dimensions at the same time)} + \item unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain) + \end{itemize} + \end{frame} + \begin{frame} + \frametitle{impact of new binning optimisation} + \begin{itemize} + \item removal of tiny bins which contribute negligible sensitivity + \item colour: limit obtained, using only this particular bin + \item number: rank of that bin (1=best sensitivity bin) + \end{itemize} + + ~ + + \begin{columns} + \begin{column}{.5\textwidth} + old analysis + + ~ + + \includegraphics[width=.95\textwidth]{./90CLonebinlimit.eps} + \end{column} + \begin{column}{.5\textwidth} + new analysis + + (2011 data, not final calibration) + \includegraphics[width=.95\textwidth]{./rank.eps} + \end{column} + \end{columns} + \end{frame} + + + \begin{frame} + \frametitle{mass shape} + \begin{itemize} + \item double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian) + \item fix fraction to ease calibration:\newline + $\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$ + \end{itemize} + \includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf} + + {\footnotesize{ + \begin{tabular}{|c|c|c|} + \hline + calibrated $\Ptau$ mass shape & 7~TeV & 8~TeV\\ + \hline + Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\ + \hline + $\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\ + \hline + $\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\ + \hline + \end{tabular} + } + } + \end{frame} + +\beamertemplateshadingbackground{darkgreen!30}{PineGreen!30} + \section{choice of triggers} + \begin{frame} + \frametitle{the story} + \begin{itemize} + \item first look at $\PDs\to\Pphi\Ppi$ revealed: signal/background much worse in 2012 + \item[$\rightarrow$] charm got more bandwidth in 2012 + \item taking all events quite unsatisfactory:\begin{itemize} + \item strictly speaking: we don't know why the events ended up on tape + \item trigger efficiencies unstable (TIS/TPS/TOS efficiencies for lots of lines and TCKs) + \item signal anyhow mostly TOS in a muon trigger + \end{itemize} + \item[$\Rightarrow$] if an event was background in the trigger, then don't consider it signal afterwards. + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{strategy} + \begin{itemize} + \item back of the envelope: limit scales with $1/\varepsilon_\text{sig}$ + \item back of the envelope: limit scales with $\sqrt{\varepsilon_\text{bkg}}$ + \item[$\Rightarrow$] minimise $FOM=\frac{\sqrt{\varepsilon_\text{bkg}}}{\varepsilon_\text{sig}}$ + \item running TCKsh and some combinatorics: $\mathcal{O}(2^{256}\approx 10^{75})$ possibilities of using HLT2 line (ignoring that there are different TCKs, TIS/TOS/TPS/DEC, \dots) + \item[$\rightarrow$] be more pragmatic! + \end{itemize} + \begin{exampleblock}{trigger optimisation} + \begin{itemize} + \item sort trigger lines (Punzi FoM) + \item start with events from the best trigger line and compute $FOM$ + \item add events from the next trigger and recompute $FOM$ + \item iterate and converge to $FOM(\text{all triggers})$ + \item use all triggers until $FOM$ starts rising. + \end{itemize} + \end{exampleblock} + \end{frame} + + \begin{frame} + \frametitle{our triggers} + {\footnotesize{ + \begin{tabular}{l|c|c} + & signal & normalisation \\\hline\hline + L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline + Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline + Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\ + & || Hlt2TriMuonTau TOS & \\\hline + Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline + \end{tabular} + } + } + \only<1>{ + \begin{block}{$^1$ triggers in 2012} + \begin{itemize} + \item cuts changed through 2012 + \item[$\rightarrow$] \textcolor{darkgreen}{emulated two different TCKs for 2012} + \end{itemize} + \end{block}} + \only<2>{ + \begin{block}{$^2$ word on Hlt2DiMuonDetached} + \begin{itemize} + \item keep it simple here + \item line unchanged in 2012 + \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable + \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification) + \end{itemize} + \end{block}} + + \end{frame} + + \begin{frame} + \frametitle{cross check (not in the note)} + \begin{itemize} + \item shouldn't the multivariate classifier do better than any trigger? + \item back-of-the-envelope overestimates the improvement (expect $\sim 9\,\%$ improvement) + \item[$\rightarrow$] add events back to the ntuple, recalculate normalisation, redid fits + \item[$\Rightarrow$] \textcolor{darkgreen}{restricting the triggers gains $\sim 3\,\%$ sensitivity wrt.\ previous round} + \end{itemize} + \end{frame} +\beamertemplateshadingbackground{White}{White} + + \section{normalisation} + + \begin{frame} + \frametitle{relative normalisation} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$ + \begin{itemize} + \item where $\varepsilon$ stands for trigger, reconstruction, selection + \item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$ + \item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$ + \newline i.e.\ $(83\pm3)\,\%$ for 2012 + \end{itemize} + \includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf} + \includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf} + \end{frame} + + \begin{frame}[allowframebreaks] + \frametitle{normalisation in numbers} + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{GEN} & 8.98 \pm 0.41 & 9.20 \pm 0.36\\ +\hline +\rm{\epsilon_{cal}}^{GEN} & 11.19 \pm 0.34 & 11.53 \pm 0.32\\ +\hline +\rm{\epsilon_{sig}}^{REC,isMuon,SEL} & 9.794 \pm 0.028 & 9.134 \pm 0.023 \\ +\hline +\rm{\epsilon_{cal}}^{REC,isMuon,SEL} & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\ +\hline +\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\ +\hline +\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\ +\hline +\rm{c}^{\Pphi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\ +\hline +\rm{c}^{\Ptau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\ +\hline +\rm{c}^{trash} & 1.95 \pm 0.12 & 2.05 \pm 0.12\\ +\hline +\rm{\epsilon\mathstrut_{sig}}^{TRIG} & 35.45 \pm 0.11 \pm 0.14 & 39.1 \pm 1.7 \pm 2.0 \\ +\hline +\rm{\epsilon\mathstrut_{cal}}^{TRIG} & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\ +\end{array}$ + }} + +\framebreak + + {\footnotesize{ +$\begin{array}{c|c|c} +& \rm{7~TeV} & \rm{8~TeV}\\ +\hline +\mathcal{B}(\PDs\to\Pphi\Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\ +\hline +f^{\Ptau}_{\PDs} & 0.82 \pm 0.03 & 0.83 \pm 0.03 \\ +\hline +\mathcal{B}(\PDs\to\Ptau\Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{REC\&SEL}/ +\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL} +& 0.897 \pm 0.061 & 0.926 \pm 0.056 \\ +\hline +\rm{\epsilon\mathstrut_{norm}}^{TRIG}/ +\rm{\epsilon\mathstrut_{sig}}^{TRIG} +& 0.6606 \pm 0.0059 & 0.527 \pm 0.041\\ +\hline +N_{norm} & 28,162 \pm 434 & 51,998 \pm 684\\ +\hline & \\[-1.5em]\hline +\alpha & (4.05 \pm 0.48) \times 10^{-9} & (1.83 \pm 0.25) \times 10^{-9}\\ +\alpha^{trash} & (7.90 \pm 0.49) \times 10^{-9} & (3.75 \pm 0.27) \times 10^{-9}\\ +\end{array}$ +}} + \end{frame} + + + \section{backgrounds} + + \begin{frame} + \frametitle{misidentification} + \begin{itemize} + \item most dominant: $\PDplus\to\PK\Ppi\Ppi$ + \item experience from last round: cut away low ProbNNmu range + \item check remaining data under $\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak + \item[$\Rightarrow$] misid safely contained in ``trash'' bin + \item \textcolor{darkgreen}{$\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$ start to become visible in 2012} + \end{itemize} + \includegraphics[width=.45\textwidth]{./Dp2Kpipi_all_2012_senseBins.pdf} + \includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf} + \end{frame} + + \begin{frame} + \frametitle{evil backgrounds} + \begin{itemize} + \item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass + \item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy + \begin{itemize} + \item modelled in CONF note + \item optimised veto in PAPER + \item right now: both versions in the ANA note + \end{itemize} + \item baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$ + \begin{itemize} + \item fits better understood + \item sensitivity unchanged when removing veto + \item smaller uncertainty on expected background + \end{itemize} + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{remaining backgrounds} + \begin{itemize} + \item fit exponential to invariant mass spectrum in each likelihood bin + \item don't use $\pm \unit{30}{\MeV}$ in the fit + \item[$\rightarrow$] compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier developement} + \end{itemize} + {\begin{center} + most sensitive bins in 2011 and 2012 + \includegraphics[width=.4\textwidth]{./fit2011.png} + \includegraphics[width=.4\textwidth]{./fit2012.png} + \end{center}} + \end{frame} + + \section{results} + + \begin{frame} + \frametitle{expected limit} + \begin{itemize} + \item still blinded + \item consider nuisance parameters from background fit, signal pdf calibration, normalisation + \item nuisance parameters due to $\Ptau$ production not included in signal pdf shape, yet + \item limit for combined 2011+2012 analysis + \end{itemize} + \end{frame} + + \begin{frame} + \frametitle{sensitivity} + $\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.6 \times 10^{-8}$ at 90\% CL + + \includegraphics[width=.8\textwidth]{./banana.png} + \end{frame} + +\beamertemplateshadingbackground{PineGreen!30}{White} + \section{model dependence} + + \begin{frame} + \frametitle{model dependence} + \begin{itemize} + \item $\Peta$ veto $\Rightarrow$ our limit not applicable to New Physics with small $m_{\APmuon\Pmuon}$ + \item model independent description in \texttt{arXiv:0707.0988} + \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms + \end{itemize} + \only<2->{ + \begin{itemize} + \item with radiative distribution limit gets worse by $51\,\%$ (dominantly from the $\Peta$ veto) + \item the other four Dalitz distributions behave nicely (within $7\,\%$) + \end{itemize} + } + \only<1>{ + \includegraphics[width=.331\textwidth]{./gammallll.eps} + \includegraphics[width=.331\textwidth]{./gammallrr.eps} + \includegraphics[width=.331\textwidth]{./gammarad.eps} + + \includegraphics[width=.331\textwidth]{./gammarad-llll.eps} + \includegraphics[width=.331\textwidth]{./gammarad-llrr.eps} +} + + \end{frame} + +\beamertemplateshadingbackground{White}{White} + + \begin{frame} + \frametitle{Conclusion} + \begin{columns} + \begin{column}{.55\textwidth} + \begin{itemize} + \item finally all pieces put together + \item model (in)dependence of $\Peta$ veto investigated + \item expected sensitivity computed\newline $5.6\times 10^{-8}$ + \end{itemize} + \end{column} + \begin{column}{.45\textwidth} + \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg} + \end{column} + \end{columns} + + \end{frame} + \end{document} diff --git a/tau23mu_lhcb/09_10_2014/xwindow.png b/tau23mu_lhcb/09_10_2014/xwindow.png new file mode 100644 index 0000000..f43cc7e --- /dev/null +++ b/tau23mu_lhcb/09_10_2014/xwindow.png Binary files differ