Newer
Older
Presentations / Seminars / UJ / mchrzasz.tex
@Marcin Chrzaszcz Marcin Chrzaszcz on 2 Jan 2018 72 KB Finished UJ seminar
  1. \documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer}
  2.  
  3. \usepackage[english]{babel}
  4. \usepackage{polski}
  5.  
  6.  
  7. \usetheme[
  8. bullet=circle, % Other option: square
  9. bigpagenumber, % circled page number on lower right
  10. topline=true, % colored bar at the top of the frame
  11. shadow=false, % Shading for beamer blocks
  12. watermark=BG_lower, % png file for the watermark
  13. ]{Flip}
  14.  
  15. %\logo{\kern+1.em\includegraphics[height=1cm]{SHiP-3_LightCharcoal}}
  16.  
  17.  
  18. \usepackage[lf]{berenis}
  19. \usepackage[LY1]{fontenc}
  20. \usepackage[utf8]{inputenc}
  21.  
  22. %\usepackage{emerald}
  23. \usefonttheme{professionalfonts}
  24. \usepackage[no-math]{fontspec}
  25. \defaultfontfeatures{Mapping=tex-text} % This seems to be important for mapping glyphs properly
  26.  
  27. \setmainfont{Gillius ADF} % Beamer ignores "main font" in favor of sans font
  28. \setsansfont{Gillius ADF} % This is the font that beamer will use by default
  29. % \setmainfont{Gill Sans Light} % Prettier, but harder to read
  30.  
  31. \setbeamerfont{title}{family=\fontspec{Gillius ADF}}
  32.  
  33. \input t1augie.fd
  34.  
  35. %\newcommand{\handwriting}{\fontspec{augie}} % From Emerald City, free font
  36. %\newcommand{\handwriting}{\usefont{T1}{fau}{m}{n}} % From Emerald City, free font
  37. % \newcommand{\handwriting}{} % If you prefer no special handwriting font or don't have augie
  38.  
  39. %% Gill Sans doesn't look very nice when boldfaced
  40. %% This is a hack to use Helvetica instead
  41. %% Usage: \textbf{\forbold some stuff}
  42. %\newcommand{\forbold}{\fontspec{Arial}}
  43.  
  44. \usepackage{graphicx}
  45. \usepackage[export]{adjustbox}
  46.  
  47. \usepackage{amsmath}
  48. \usepackage{amsfonts}
  49. \usepackage{amssymb}
  50. \usepackage{bm}
  51. \usepackage{colortbl}
  52. \usepackage{mathrsfs} % For Weinberg-esque letters
  53. \usepackage{cancel} % For "SUSY-breaking" symbol
  54. \usepackage{slashed} % for slashed characters in math mode
  55. \usepackage{bbm} % for \mathbbm{1} (unit matrix)
  56. \usepackage{amsthm} % For theorem environment
  57. \usepackage{multirow} % For multi row cells in table
  58. \usepackage{arydshln} % For dashed lines in arrays and tables
  59. \usepackage{siunitx}
  60. \usepackage{xhfill}
  61. \usepackage{grffile}
  62. \usepackage{textpos}
  63. \usepackage{subfigure}
  64. \usepackage{tikz}
  65.  
  66. %\usepackage{hepparticles}
  67. \usepackage[italic]{hepparticles}
  68.  
  69. \usepackage{hepnicenames}
  70.  
  71. % Drawing a line
  72. \tikzstyle{lw} = [line width=20pt]
  73. \newcommand{\topline}{%
  74. \tikz[remember picture,overlay] {%
  75. \draw[crimsonred] ([yshift=-23.5pt]current page.north west)
  76. -- ([yshift=-23.5pt,xshift=\paperwidth]current page.north west);}}
  77.  
  78.  
  79.  
  80. % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
  81. \usepackage{tikzfeynman} % For Feynman diagrams
  82. \usetikzlibrary{arrows,shapes}
  83. \usetikzlibrary{trees}
  84. \usetikzlibrary{matrix,arrows} % For commutative diagram
  85. % http://www.felixl.de/commu.pdf
  86. \usetikzlibrary{positioning} % For "above of=" commands
  87. \usetikzlibrary{calc,through} % For coordinates
  88. \usetikzlibrary{decorations.pathreplacing} % For curly braces
  89. % http://www.math.ucla.edu/~getreuer/tikz.html
  90. \usepackage{pgffor} % For repeating patterns
  91.  
  92. \usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams
  93. \usetikzlibrary{decorations.markings}
  94. \tikzset{
  95. % >=stealth', %% Uncomment for more conventional arrows
  96. vector/.style={decorate, decoration={snake}, draw},
  97. provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw},
  98. antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw},
  99. fermion/.style={draw=gray, postaction={decorate},
  100. decoration={markings,mark=at position .55 with {\arrow[draw=gray]{>}}}},
  101. fermionbar/.style={draw=gray, postaction={decorate},
  102. decoration={markings,mark=at position .55 with {\arrow[draw=gray]{<}}}},
  103. fermionnoarrow/.style={draw=gray},
  104. gluon/.style={decorate, draw=black,
  105. decoration={coil,amplitude=4pt, segment length=5pt}},
  106. scalar/.style={dashed,draw=black, postaction={decorate},
  107. decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}},
  108. scalarbar/.style={dashed,draw=black, postaction={decorate},
  109. decoration={markings,mark=at position .55 with {\arrow[draw=black]{<}}}},
  110. scalarnoarrow/.style={dashed,draw=black},
  111. electron/.style={draw=black, postaction={decorate},
  112. decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}},
  113. bigvector/.style={decorate, decoration={snake,amplitude=4pt}, draw},
  114. }
  115.  
  116. % TIKZ - for block diagrams,
  117. % from http://www.texample.net/tikz/examples/control-system-principles/
  118. % \usetikzlibrary{shapes,arrows}
  119. \tikzstyle{block} = [draw, rectangle,
  120. minimum height=3em, minimum width=6em]
  121.  
  122.  
  123.  
  124.  
  125. \usetikzlibrary{backgrounds}
  126. \usetikzlibrary{mindmap,trees} % For mind map
  127. \newcommand{\degree}{\ensuremath{^\circ}}
  128. \newcommand{\E}{\mathrm{E}}
  129. \newcommand{\Var}{\mathrm{Var}}
  130. \newcommand{\Cov}{\mathrm{Cov}}
  131. \newcommand\Ts{\rule{0pt}{2.6ex}} % Top strut
  132. \newcommand\Bs{\rule[-1.2ex]{0pt}{0pt}} % Bottom strut
  133.  
  134. \graphicspath{{images/}} % Put all images in this directory. Avoids clutter.
  135.  
  136. % SOME COMMANDS THAT I FIND HANDY
  137. % \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec
  138. \newcommand{\comment}[1]{\textcolor{comment}{\footnotesize{#1}\normalsize}} % comment mild
  139. \newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold
  140. \newcommand{\COMMENT}[1]{\textcolor{COMMENT}{\footnotesize{#1}\normalsize}} % comment crazy bold
  141. \newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert
  142. \newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert
  143. %% "\alert" is already a beamer pre-defined
  144. \newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}%
  145.  
  146. \def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}}
  147.  
  148. \usepackage{gmp}
  149. \usepackage[final]{feynmp-auto}
  150.  
  151. \usepackage[backend=bibtex,style=numeric-comp,firstinits=true]{biblatex}
  152. \bibliography{bib}
  153. \setbeamertemplate{bibliography item}[text]
  154.  
  155. \makeatletter\let\frametextheight\beamer@frametextheight\makeatother
  156.  
  157. % suppress frame numbering for backup slides
  158. % you always need the appendix for this!
  159. \newcommand{\backupbegin}{
  160. \newcounter{framenumberappendix}
  161. \setcounter{framenumberappendix}{\value{framenumber}}
  162. }
  163. \newcommand{\backupend}{
  164. \addtocounter{framenumberappendix}{-\value{framenumber}}
  165. \addtocounter{framenumber}{\value{framenumberappendix}}
  166. }
  167.  
  168.  
  169. \definecolor{links}{HTML}{2A1B81}
  170. %\hypersetup{colorlinks,linkcolor=,urlcolor=links}
  171.  
  172. % For shapo's formulas:
  173. \def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
  174. \def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
  175. \newcommand{\lsim}{\mathop{\lsi}}
  176. \newcommand{\gsim}{\mathop{\gsi}}
  177. \newcommand{\wt}{\widetilde}
  178. %\newcommand{\ol}{\overline}
  179. \newcommand{\Tr}{\rm{Tr}}
  180. \newcommand{\tr}{\rm{tr}}
  181. \newcommand{\eqn}[1]{&\hspace{-0.7em}#1\hspace{-0.7em}&}
  182. \newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}}
  183. \newcommand{\abs}[1]{\rm{$\left| #1 \right|$}}
  184. \newcommand{\eV}{\rm{eV}}
  185. \newcommand{\keV}{\rm{keV}}
  186. \newcommand{\GeV}{\rm{GeV}}
  187. \newcommand{\MeV}{\rm{MeV}}
  188. \newcommand{\im}{\rm{Im}}
  189. \newcommand{\re}{{\rm Re}}
  190. \newcommand{\invfb}{\rm{fb^{-1}}}
  191. \newcommand{\fixme}{\rm{{\color{red}{FIXME!}}}}
  192. \newcommand{\thetal}{\theta_l}
  193. \newcommand{\thetak}{\theta_k}
  194. \newcommand{\nn}{\nonumber}
  195. \newcommand{\eq}[1]{\begin{equation} #1 \end{equation}}
  196. %\newcommand{\eqn}[1]{\begin{displaymath} #1 \end{displaymath}}
  197. \newcommand{\eqa}[1]{\begin{eqnarray} #1 \end{eqnarray}}
  198. \newcommand{\apeL}{{A_\perp^L}}
  199. \newcommand{\apeR}{{A_\perp^R}}
  200. \newcommand{\apeLR}{{A_\perp^{L,R}}}
  201. \newcommand{\apaL}{{A_\|^L}}
  202. \newcommand{\apaR}{{A_\|^R}}
  203. \newcommand{\apaLR}{{A_\|^{L,R}}}
  204. \newcommand{\azeL}{{A_0^L}}
  205. \newcommand{\azeR}{{A_0^R}}
  206. \newcommand{\azeLR}{{A_0^{L,R}}}
  207. \newcommand{\Real}{\ensuremath{\mathcal{R}e}\xspace}
  208. \newcommand{\Imag}{\ensuremath{\mathcal{I}m}\xspace}
  209.  
  210. \renewcommand{\C}[1]{{\cal C}_{#1}}
  211. \newcommand{\Ceff}[1]{{\cal C}^{\rm eff}_{#1}}
  212. \newcommand{\Cpeff}[1]{{\cal C}^{\rm eff\prime}_{#1}}
  213. \newcommand{\Cp}[1]{{\cal C}^{\prime}_{#1}}
  214. \def\FL {\ensuremath{F_{\mathrm{L}}}\xspace}
  215. \def\ATDPH {\ensuremath{A_{\mathrm{T,PR}}^{(2)}}\xspace}
  216. \def\ATImPH {\ensuremath{A_{\mathrm{T,PR}}^{\mathrm{Im}}}\xspace}
  217. \def\ATRePH {\ensuremath{A_{\mathrm{T,PR}}^{\mathrm{Re}}}\xspace}
  218. \def\FLPH {\ensuremath{F_{\mathrm{L,PR}}}\xspace}
  219. \def\ATDKG {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{(2)}}\xspace}
  220. \def\ATImKG {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{\mathrm{Im}}}\xspace}
  221. \def\ATReKG {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{\mathrm{Re}}}\xspace}
  222. \def\FLKG {\ensuremath{F_{\mathrm{L,\Kstarz \gamma}}}\xspace}
  223. \def\ATD {\ensuremath{A_{\mathrm{T}}^{(2)}}\xspace}
  224. \def\ATIm {\ensuremath{A_{\mathrm{T}}^{\mathrm{Im}}}\xspace}
  225. \def\ATRe {\ensuremath{A_{\mathrm{T}}^{\mathrm{Re}}}\xspace}
  226. \def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace}
  227.  
  228.  
  229.  
  230. \newcommand{\disp}{\displaystyle}
  231. \def\be{\begin{equation}}
  232. \def\ee{\end{equation}}
  233. \def\ba{\begin{eqnarray}}
  234. \def\ea{\end{eqnarray}}
  235. \def\d{\partial}
  236. \def\l{\left(}
  237. \def\r{\right)}
  238. \def\la{\langle}
  239. \def\ra{\rangle}
  240. \def\e{{\rm e}}
  241. \def\Br{{\rm Br}}
  242.  
  243. \newcommand{\av}[1]{\langle #1 \rangle}
  244. % particles
  245. \def\LstFTTT {\ensuremath{\PLambda^{*}(1520)^{0}}\xspace}
  246. \def\dll {\ensuremath{\mathrm{DLL}}\xspace}
  247. \def\Lb {\ensuremath{\PLambda_b}}
  248.  
  249.  
  250. % useful decays
  251. \def\BdToKpimm {\decay{\Bd}{\Kp\pim\mumu}}
  252. \def\BuToKmm {\decay{\Bu}{\Kp\mumu}}
  253. \def\BsToJPsiKst {\decay{\Bs}{\jpsi\Kstarz}}
  254. \def\BdTopsitwosKst {\decay{\Bd}{\psitwos\Kstarz}}
  255. \def\LstFTTTT {\decay{\LstFTTT}{p\Km}}
  256. %\def\LbToLstmm {\decay{\Lb}{\PLambda^{*}(1520)^{0} \mumu}}
  257. \def\LbTopKmm {\decay{\Lb}{p\Km\mumu}}
  258. \def\BuToKmm {\decay{\Bu}{\Kp\mumu}}
  259. \def\BsTophimm {\decay{\Bs}{\Pphi\mumu}}
  260. % interesting variables
  261. \def\mkpi {\ensuremath{m_{K\pi}}\xspace}
  262. \def\mkpimm{\ensuremath{m_{K\pi\mu\mu}}\xspace}
  263. %% peaking background mass hypotheses
  264. \def\mkmm {\ensuremath{m_{K\mu\mu}}\xspace}
  265. \def\mSwappKmm {\ensuremath{m_{(\pi\to p)K\mu\mu}}\xspace}
  266. \def\mSwappiK {\ensuremath{m_{(\pi\to K)K}}\xspace}
  267. \def\mSwappiKmm {\ensuremath{m_{(\pi\to K)K\mu\mu}}\xspace}
  268. \def\mSwappK {\ensuremath{m_{(\pi\to p)K}}\xspace}
  269. \def\mDoubleSwappKmm {\ensuremath{m_{(K\to p)(\pi\to K)\mu\mu}}\xspace}
  270. \def\mDoubleSwappK {\ensuremath{m_{(K\to p)(\pi\to K)}}\xspace}
  271. \def\mSwapKst {\ensuremath{m_{K\leftrightarrow\pi}}\xspace}
  272. %% some other decays
  273. \def\BsToPhimm {\decay{\Bs}{\phi\mumu}}
  274. \def\BsToPhimmFULL {\decay{\Bs}{\phi(\to\!K^{+}K^{-})\mumu}}
  275. \def\BsToKKmm {\decay{\Bs}{\Kp\Km\mumu}}
  276.  
  277. \newcommand{\delC}[1]{\delta {\cal C}_{#1}}
  278. \newcommand{\dC}[1]{{\cal C}_{#1}^{\rm NP}}
  279. \newcommand{\dCp}[1]{{\cal C}_{#1^\prime}^{\rm NP}}
  280.  
  281.  
  282.  
  283.  
  284. \definecolor{green}{rgb}{0.2,0.6,0.2}
  285. \definecolor{lightgreen}{rgb}{0.4,1,0.4}
  286. \definecolor{verylightgreen}{rgb}{0.7,1,0.7}
  287. \def\cgreen{\color{green}}
  288. \definecolor{brown}{rgb}{0.4,0.2,0.0}
  289. \def\cbrown{\color{brown}}
  290. \def\cred{\color{red}}
  291. \definecolor{darkblue}{rgb}{0.0,0.0,1.0}
  292. \def\cdarkblue{\color{darkblue}}
  293. \definecolor{darkgrey}{rgb}{0.4,0.4,0.4}
  294. \definecolor{lightgrey}{rgb}{0.7,0.7,0.7}
  295. \definecolor{verylightblue}{rgb}{0.8,0.8,1.0}
  296. \definecolor{lightblue}{rgb}{0.6,0.6,1.0}
  297. \definecolor{verylightyellow}{rgb}{1.0,1.0,0.5}
  298. \definecolor{lightyellow}{rgb}{1.0,0.7,0.3}
  299. \definecolor{darkred}{rgb}{0.6,0.0,0.0}
  300.  
  301. \definecolor{green}{rgb}{0.3,0.6,0.2}
  302. \definecolor{green}{rgb}{0.3,0.7,0.4}
  303.  
  304.  
  305.  
  306.  
  307. \definecolor{indigo}{RGB}{100,0,100}
  308. \definecolor{dgray}{RGB}{80,80,80}
  309. \definecolor{lgray}{RGB}{220,220,220}
  310. \definecolor{dred}{RGB}{190,0,0}
  311. \definecolor{dgreen}{RGB}{0,110,0}
  312. \definecolor{lyellow}{RGB}{245,245,210}
  313. \definecolor{bblue}{RGB}{93,93,255}
  314. \definecolor{bbrown}{RGB}{150,85,52}
  315. \definecolor{llgray}{RGB}{230,230,230}
  316.  
  317.  
  318.  
  319. \newcommand{\F}{\mathcal{F}}
  320. \newcommand{\A}{\mathcal{A}}
  321. \newcommand{\N}{\mathcal{N}}
  322. \renewcommand{\H}{\mathcal{H}}
  323. \newcommand{\Leff}{\mathcal{L}_{\rm eff}}
  324. \newcommand{\heff}{\mathcal{H}_{\rm eff}}
  325. \newcommand{\Lag}{\mathcal{L}}
  326. \newcommand{\red}{\color{red}}
  327. \newcommand{\blue}{\color{blue}}
  328. \newcommand{\indigo}{\color{indigo}}
  329. \newcommand{\brown}{\color{bbrown}}
  330. \newcommand{\bs}{\mathbf}
  331. \newcommand{\sss}{\scriptscriptstyle}
  332.  
  333.  
  334. \newcommand{\btr}{{ $\blacktriangleright\ $}}
  335. \institute{UZH}
  336. \title[New Physics signatures in Rare $\PB$ decays?]{New Physics signatures in Rare $\PB$ decays?}
  337. \date{25 September 2014}
  338.  
  339. \author{ Marcin Chrzaszcz (CERN, IFJ PAN)}
  340.  
  341.  
  342.  
  343. \begin{document}
  344. \tikzstyle{every picture}+=[remember picture]
  345.  
  346. {
  347. \setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
  348. \begin{frame}[c]%{\phantom{title page}}
  349. \begin{center}
  350. \begin{center}
  351. \begin{columns}
  352. \begin{column}{0.75\textwidth}
  353. \flushright \bfseries \huge {New Physics signatures \\in Rare $\PB$ decays}
  354. \end{column}
  355. \begin{column}{0.02\textwidth}
  356. {~}
  357. \end{column}
  358. \begin{column}{0.23\textwidth}
  359. % \hspace*{-1.cm}
  360. \vspace*{-3mm}
  361. \includegraphics[width=0.6\textwidth]{lhcb-logo}
  362. \end{column}
  363.  
  364. \end{columns}
  365. \end{center}
  366. \quad
  367. \vspace{3em}
  368. \begin{columns}
  369. \begin{column}{0.44\textwidth}
  370. %\flushright \vspace{-2.8em} { \fontspec{Zapfino} Marcin Chrzaszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
  371.  
  372. \flushright \vspace{-2.8em} { \Large Marcin Chrzaszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
  373.  
  374.  
  375. \end{column}
  376. \begin{column}{0.53\textwidth}
  377. \hspace{2.0cm}
  378. \includegraphics[height=1.6cm]{cern}~~
  379. \includegraphics[height=1.3cm]{ifj}
  380.  
  381. \end{column}
  382. \end{columns}
  383.  
  384. \vspace{1em}
  385.  
  386. \textcolor{normal text.fg!50!Comment}{WFAIS Seminar, Krakow\\January 8, 2018}
  387. \end{center}
  388. \end{frame}
  389. }
  390. \begin{frame}{Outline}
  391.  
  392. \begin{minipage}{\textwidth}
  393. {~}\\
  394.  
  395. \begin{enumerate}
  396. \item Why flavour is important.
  397. \item LHCb detector.
  398. \item $\Pbeauty \to \Pstrange \ell \ell$ theory in a nutshell.
  399. \item LHCb measurements of $\PB \to \PKstar \Pmu \Pmu$
  400. \begin{itemize}
  401. \item Maximum likelihood fit.
  402. \item Method of moments.
  403. \item Amplitudes fit.
  404. \end{itemize}
  405. \item Other related LHCb measurements.
  406. \item Global fit to $\Pbeauty \to \Pstrange \ell \ell$ measurements.
  407. \item Disclaimers about some theory predictions.
  408. \item Conclusions.
  409. \end{enumerate}
  410.  
  411.  
  412. \end{minipage}
  413. \vspace*{2.cm}
  414. \end{frame}
  415. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  416. % Why flavour physics
  417. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  418. \begin{frame}
  419. \begin{center}
  420. \begin{Huge}
  421. Why Flavour is important?
  422. \end{Huge}
  423. \end{center}
  424.  
  425.  
  426.  
  427.  
  428. \end{frame}
  429.  
  430.  
  431.  
  432. \begin{frame}{A lesson from history - GIM mechanism}
  433. \begin{minipage}{\textwidth}
  434.  
  435. \begin{center}
  436. \includegraphics[width=0.62\textwidth]{images/GIM2.png}
  437. \end{center}
  438. \begin{columns}
  439. \column{0.7\textwidth}
  440. \begin{itemize}
  441. \begin{footnotesize}
  442.  
  443.  
  444. \item Cabibbo angle was successful in explaining dozens of decay rates in the 1960s.
  445. \item There was, however, one that was not observed by experiments: $\PKzero \to \Pmuon \APmuon$.
  446. \item Glashow, Iliopoulos, Maiani (GIM) mechanism was proposed in the 1970 to fix this problem. The mechanism required the existence of a $4^{th}$ quark.
  447. \item At that point most of the people were skeptical about that. Fortunately in 1974 the discovery of the $\PJpsi$ meson silenced the skeptics.
  448. \end{footnotesize}
  449. \end{itemize}
  450. \column{0.3\textwidth}
  451. \begin{center}
  452. \includegraphics[width=0.95\textwidth]{images/GIM3.png}\\
  453. \includegraphics[width=0.7\textwidth]{images/604.jpg}\\{~}\\{~}
  454. \end{center}
  455. \end{columns}
  456.  
  457.  
  458.  
  459. \end{minipage}
  460.  
  461. \vspace*{2.1cm}
  462. \end{frame}
  463.  
  464. \begin{frame}{A lesson from history - CKM matrix}
  465. \begin{minipage}{\textwidth}
  466.  
  467. \begin{center}
  468. {~}\\{~}\\
  469. \includegraphics[width=0.5\textwidth]{images/CKMmatrix.png}
  470.  
  471. \end{center}
  472. \begin{columns}
  473. \column{0.6\textwidth}
  474. \begin{itemize}
  475. \begin{small}
  476.  
  477.  
  478.  
  479.  
  480. \item Similarly, CP violation was discovered in 1960s in the neutral kaons decays.
  481. \item $2 \times 2$ Cabbibo matrix could not allow for any CP violation.
  482. \item For CP violation to be possible one needs at least a $3 \times 3$ unitary matrix \\ $\looparrowright$ Cabibbo-Kobayashi-Maskawa matrix (1973).
  483. \item It predicts existence of $\Pbottom$ (1977) and $\Ptop$ (1995) quarks.
  484. \end{small}
  485.  
  486. \end{itemize}
  487. \column{0.4\textwidth}
  488. \begin{center}
  489. {~}
  490. %\includegraphics[height=2cm]{images/CP.png}\\
  491. \includegraphics[width=0.96\textwidth]{bottom.jpg}
  492.  
  493. \end{center}
  494. \end{columns}
  495.  
  496.  
  497.  
  498. \end{minipage}
  499.  
  500. \vspace*{2.1cm}
  501. \end{frame}
  502.  
  503.  
  504. \begin{frame}{A lesson from history - Weak neutral current}
  505. \begin{minipage}{\textwidth}
  506.  
  507. \begin{center}
  508. \includegraphics[height=3cm]{images/weakcurr.png}{~}
  509. \includegraphics[height=3cm]{images/weakcurr2.png}
  510. \end{center}
  511.  
  512. \begin{columns}
  513. \column{0.6\textwidth}
  514. \begin{itemize}
  515. \begin{small}
  516.  
  517.  
  518. \item Weak neutral currents were first introduced in 1958 by Buldman.
  519. \item Later on they were naturally incorporated into unification of weak and electromagnetic interactions.
  520. \item 't Hooft proved that the GWS models was renormalizable.
  521. \item Everything was there on theory side, only missing piece was the experiment, till 1973.
  522. \end{small}
  523.  
  524. \end{itemize}
  525. \column{0.4\textwidth}
  526. \begin{center}
  527. {~}
  528. %\includegraphics[height=2cm]{images/CP.png}\\
  529. \includegraphics[width=0.85\textwidth]{images/bubblecern.png}
  530. \end{center}
  531. \end{columns}
  532.  
  533.  
  534.  
  535. \end{minipage}
  536.  
  537. \vspace*{2.1cm}
  538. \end{frame}
  539.  
  540. \begin{frame}
  541. \begin{center}
  542. \begin{Huge}
  543. LHCb detector
  544. \end{Huge}
  545. \end{center}
  546.  
  547.  
  548.  
  549.  
  550. \end{frame}
  551.  
  552. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  553. % DETECTOR
  554. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  555. \begin{frame}
  556. \only<1>{\frametitle{LHCb detector - tracking}
  557. \begin{columns}
  558. \column{3in}
  559. \includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
  560.  
  561. \column{2in}
  562. \includegraphics[width=0.95\textwidth]{images/sketch.png}
  563. \end{columns}
  564. \begin{itemize}
  565. \item Excellent Impact Parameter (IP) resolution ($20~\rm \mu m$).\\
  566. $\Rightarrow$ Identify secondary vertices from heavy flavour decays
  567. \item Proper time resolution $\sim~40~\rm fs$.\\
  568. $\Rightarrow$ Good separation of primary and secondary vertices.
  569. \item Excellent momentum ($\delta p/p \sim 0.4 - 0.6\%$) and inv. mass resolution.\\
  570. $\Rightarrow$ Low combinatorial background.
  571.  
  572. \end{itemize}
  573.  
  574.  
  575. }
  576.  
  577. \only<2>{\frametitle{LHCb detector - particle identification}
  578. \begin{columns}
  579. \column{3in}
  580. \includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
  581.  
  582. \column{2in}
  583. \includegraphics[width=0.95\textwidth]{images/cher.png}
  584. \end{columns}
  585. \begin{itemize}
  586. \item Excellent Muon identification $\epsilon_{\mu \to \mu} \sim 97\%$, $\epsilon_{\pi \to \mu} \sim 1-3\%$
  587. \item Good $\PK-\Ppi$ separation via RICH detectors, $\epsilon_{\PK \to \PK} \sim 95\%$, $\epsilon_{\Ppi \to \PK} \sim 5\%$.\\
  588. $\Rightarrow$ Reject peaking backgrounds.
  589. \item High trigger efficiencies, low momentum thresholds.
  590. Muons: $p_T > 1.76 \GeV$ at L0, $p_T > 1.0 \GeV$ at HLT1,\\
  591. $B \to \PJpsi X $: Trigger $\sim 90\%$.
  592.  
  593. \end{itemize}
  594.  
  595.  
  596. }
  597.  
  598.  
  599. \end{frame}
  600.  
  601.  
  602.  
  603.  
  604.  
  605. \iffalse
  606.  
  607.  
  608. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  609. \begin{frame}{Modern challenges: loops come in to the game}
  610. \begin{minipage}{\textwidth}
  611. \begin{columns}
  612.  
  613. \column{0.5\textwidth}
  614. \begin{itemize}
  615. \item Standard Model contributions suppressed or absent:
  616. \begin{itemize}
  617. \item Flavour Changing Neutral Currents.
  618. \item CP violation
  619. \item Lepton Flavour/Number or Lepton Universality violation.
  620. \end{itemize}
  621. \item In general can probe physics beyond General Purpose Detectors reach.
  622. \end{itemize}
  623. \column{0.5\textwidth}
  624. \includegraphics[width=0.99\textwidth]{{images/TauLFV_UL_2014001_averaged}.png}
  625.  
  626.  
  627. \end{columns}
  628. \begin{center}
  629. \includegraphics[width=0.75\textwidth]{images/Bsmumu.png}
  630. \includegraphics[width=0.20\textwidth]{{images/bsmumu_SM}.png}
  631. \end{center}
  632. \end{minipage}
  633.  
  634. \vspace*{2.1cm}
  635. \end{frame}
  636. \fi
  637.  
  638. \begin{frame}
  639. \begin{center}
  640. \begin{Huge}
  641. $\Pbeauty \to \Pstrange \ell \ell$ theory in a nutshell.
  642. \end{Huge}
  643. \end{center}
  644.  
  645.  
  646.  
  647.  
  648. \end{frame}
  649.  
  650.  
  651.  
  652.  
  653. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  654. \begin{frame}\frametitle{Why rare decays?}
  655.  
  656. \begin{columns}
  657. \column{4in}
  658. \begin{itemize}
  659. \item The SM allows only the charged interactions to change flavour.
  660. \begin{itemize}
  661. \item Other interactions are flavour conserving.
  662. \end{itemize}
  663. \item One can escape this constraint and produce $\Pbottom \to \Pstrange$ and $\Pbottom \to \Pdown$ at loop level.
  664. \begin{itemize}
  665. \item These kind of processes are suppressed in SM $\to$~Rare decays.
  666. \item New Physics can enter in the loops.
  667. \end{itemize}
  668. \end{itemize}
  669. \begin{center}
  670. \includegraphics[scale=0.3]{lupa.png}
  671. \includegraphics[scale=0.3]{example.png}
  672. \end{center}
  673. \column{1.5in}
  674. \includegraphics[width=0.61\textwidth]{couplings.png}
  675. \end{columns}
  676. \end{frame}
  677.  
  678.  
  679. \iffalse
  680.  
  681. \begin{frame}{Tools in rare $\PBzero$ decays}
  682. {~}
  683. \begin{minipage}{\textwidth}
  684.  
  685. \begin{itemize}
  686. \item \textbf{Operator Product Expansion and Effective Field Theory}
  687. \end{itemize}
  688. \begin{columns}
  689. \column{0.1in}{~}
  690. \column{3.2in}
  691. \begin{footnotesize}
  692.  
  693.  
  694. \begin{align*}
  695. H_{eff} = - \dfrac{4G_f}{\sqrt{2}} V V^{\prime \ast}\ \sum_i \left[\underbrace{C_i(\mu)O_i(\mu)}_\text{left-handed} +\
  696. \underbrace{C'_i(\mu)O'_i(\mu)}_\text{right-handed}\right],
  697. \end{align*}
  698. \end{footnotesize}
  699. \column{2in}
  700. \begin{tiny}
  701. \begin{description}
  702. \item[i=1,2] Tree
  703. \item[i=3-6,8] Gluon penguin
  704. \item[i=7] Photon penguin
  705. \item[i=9.10] EW penguin
  706. \item[i=S] Scalar penguin
  707. \item[i=P] Pseudoscalar penguin
  708. \end{description}
  709.  
  710. \end{tiny}
  711. \end{columns}
  712. where $C_i$ are the Wilson coefficients and $O_i$ are the corresponding effective operators.
  713. \begin{center}
  714. \includegraphics[width=0.85\textwidth,height=3cm]{images/all.png}
  715.  
  716. \end{center}
  717.  
  718.  
  719.  
  720.  
  721.  
  722. \end{minipage}
  723. \vspace*{2.1cm}
  724. \end{frame}
  725.  
  726. \fi
  727.  
  728.  
  729. \begin{frame}{Analysis of Rare decays}
  730. \begin{footnotesize}
  731.  
  732. %{\Large Since a long time ago...} \\ \medskip
  733. %\hspace*{1.4cm}$\Rightarrow$ $b \to s \gamma$ and $b \to s \ell\ell $ {\bf Flavour Changing Neutral Currents} have been used as {\bf \cred Our Portal} \\ to explore the fundamental theory beyond SM. \\
  734. %\medskip
  735. %\medskip
  736. %\hfill....... with not much success till 2013.\hspace*{1cm}
  737. %\bigskip
  738.  
  739. Analysis of FCNC in a model-independent approach, effective Hamiltonian:
  740. \vspace*{-0.1cm}
  741. \begin{columns}
  742. \begin{column}{1cm}
  743. ~
  744. \end{column}
  745. \begin{column}{8cm}
  746. \begin{equation*}
  747. b\to s\gamma(^*): {\mathcal H}^{SM}_{\Delta F=1} \propto
  748. \sum_{i=1}^{10} V_{ts}^* V_{tb} {\cgreen \C{i}} \alert{ {\cal O}_i} + \ldots
  749. \end{equation*}
  750.  
  751. \vspace{-0.2cm}
  752.  
  753. \begin{itemize}
  754. \item $\alert{ {\cal O}_7} = \frac{e}{16 \pi^2}m_b\,
  755. (\bar s\sigma^{\mu\nu} P_R b) F_{\mu\nu}\,$ %\quad [real or soft photon]
  756. \item $\alert{ {\cal O}_9}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b)\ (\bar\ell\gamma_\mu\ell)$
  757. %\quad [$b\to s\mu\mu$ via $Z$/hard $\gamma$]
  758. \item $\alert{ {\cal O}_{10}}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b) \ (\bar\ell\gamma_\mu\gamma_5\ell)$, ...
  759. %\quad [$b\to s\mu\mu$ via $Z$]
  760. \end{itemize}
  761. \end{column}
  762. \begin{column}{5.5cm}
  763. \includegraphics[width=3.5cm]{images/qum1.png}
  764. %\includegraphics[width=3cm]{bsll.pdf}
  765. \end{column}
  766. \end{columns}
  767.  
  768. %\hspace*{5cm} with no clear success yet...
  769. %\bigskip
  770.  
  771.  
  772. %\centerline{{\bf Goal}: \underline{Decode the short distance physics to find a smoking gun of BSM}\hspace*{2cm}}
  773.  
  774.  
  775. \bigskip
  776. \hspace*{0.0cm} $\bullet$ {\bf SM} Wilson coefficients up to NNLO + e.m. corrections at $\mu_{ref}=4.8$ GeV [{\cgreen Misiak et al.}]: $${\cal C}_7^{\rm SM}=-0.29,\, {\cal C}_9^{\rm SM}=4.1,\, {\cal C}_{10}^{\rm SM}=-4.3$$
  777. %BUT, like in the film there is always the good, the bad and the ugly.
  778. \bigskip
  779. $\bullet$ {\bf NP} changes short distance ${\cal C}_i-{\cal C}_i^{\rm SM}={\cal C}_i^{\rm NP}$ and induce new operators, like ${\cal O}^\prime_{7,9,10}={\cal O}_{7,9,10}\,\, (P_L \leftrightarrow P_R)$ ... also scalars, pseudoescalar, tensor operators...%\bigskip
  780.  
  781.  
  782. \end{footnotesize}
  783.  
  784. \end{frame}
  785.  
  786. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  787.  
  788.  
  789. \iffalse
  790. %%%%%%%%%%%%%%%%%%%%5
  791. \begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$, where it all begun}
  792. {~}
  793. \begin{minipage}{\textwidth}
  794. \only<1>{
  795. \begin{columns}
  796. \column{0.6\textwidth}
  797. August 2013:\\
  798.  
  799. \includegraphics[width=0.95\textwidth]{images/P5prime.png}
  800. \column{0.4\textwidth}
  801. \begin{itemize}
  802. \item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
  803. \item It turned out that the discrepancy occurred in an observable that was not constrained.
  804. \item $q^2$ is the dimuon invariant mass.
  805.  
  806. \end{itemize}
  807. \end{columns}
  808.  
  809.  
  810. }
  811.  
  812.  
  813.  
  814.  
  815. \only<2>{
  816.  
  817.  
  818. \begin{columns}
  819. \column{0.6\textwidth}
  820. August 2013:\\
  821.  
  822. \includegraphics[width=0.95\textwidth]{images/P5prime.png}
  823. \column{0.4\textwidth}
  824. \begin{itemize}
  825. \item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
  826. \item It turned out that the discrepancy occurred in an observable that was not constrained.
  827.  
  828. \end{itemize}
  829. \end{columns}
  830.  
  831.  
  832. \begin{exampleblock}{}
  833. Now let's move back and see the theory behind the $\PBzero \to \PKstar \Pmuon \APmuon$ and $P_5^{\prime}$.
  834. \end{exampleblock}
  835. }
  836.  
  837. \end{minipage}
  838. \vspace*{2.1cm}
  839. \end{frame}
  840.  
  841. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  842. \fi
  843.  
  844.  
  845.  
  846. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  847. \begin{frame}{$\PB \to \PKstar \Pmuon \APmuon$ kinematics}
  848. {~}
  849. \begin{minipage}{\textwidth}
  850.  
  851. $\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.
  852.  
  853. \only<1>{
  854. \begin{columns}
  855. \column{0.5\textwidth}
  856.  
  857. $\color{JungleGreen}{\Rrightarrow}$ $\cos \thetak$: the angle between the direction of the kaon in the $\PKstar$ ($\overline{\PKstar}$) rest frame and the direction of the $\PKstar$ ($\overline{\PKstar}$) in the $\PBzero$ ($\APBzero$) rest frame.\\
  858. $\color{JungleGreen}{\Rrightarrow}$ $\cos \thetal$: the angle between the direction of the $\Pmuon$ ($\APmuon$) in the dimuon rest frame and the direction of the dimuon in the $\PBzero$ ($\APBzero$) rest frame.\\
  859. $\color{JungleGreen}{\Rrightarrow}$ $\phi$: the angle between the plane containing the $\Pmuon$ and $\APmuon$ and the plane containing the kaon and pion from the $\PKstar$.
  860.  
  861.  
  862.  
  863. \column{0.5\textwidth}
  864. \includegraphics[width=0.95\textwidth]{images/angles.png}
  865.  
  866. \end{columns}
  867. }
  868. \only<2>{
  869. {\tiny{
  870. \eqa{\label{dist}
  871. \frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi}&=&\frac9{32\pi} \bigg[
  872. J_{1s} \sin^2\theta_K + J_{1c} \cos^2\theta_K + (J_{2s} \sin^2\theta_K + J_{2c} \cos^2\theta_K) \cos 2\theta_l\nn\\[1.5mm]
  873. &&\hspace{-2.7cm}+ J_3 \sin^2\theta_K \sin^2\theta_l \cos 2\phi + J_4 \sin 2\theta_K \sin 2\theta_l \cos\phi + J_5 \sin 2\theta_K \sin\theta_l \cos\phi \nn\\[1.5mm]
  874. &&\hspace{-2.7cm}+ (J_{6s} \sin^2\theta_K + {J_{6c} \cos^2\theta_K}) \cos\theta_l
  875. + J_7 \sin 2\theta_K \sin\theta_l \sin\phi + J_8 \sin 2\theta_K \sin 2\theta_l \sin\phi \nn\\[1.5mm]
  876. &&\hspace{-2.7cm}+ J_9 \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,,
  877. \nonumber}
  878. }}
  879. $\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decay.\\
  880. \pause
  881.  
  882. $\color{JungleGreen}{\Rrightarrow}$ In practice as experimentalist we do not measure $J_i$ but:
  883. \begin{columns}
  884. \column{0.5\textwidth}
  885. \ARROW Branching fraction:
  886. $\mathcal{B}(\PB \to \PKstar \Pmuon \APmuon) = 3J_{1c}+6J_{1s} - J_{2c} -2 J_{2s}$
  887. \column{0.5\textwidth}
  888. \ARROW \small Normalized angular observables:
  889. \begin{equation}
  890. S_i= \frac{J_i}{3J_{1c}+6J_{1s} - J_{2c} -2 J_{2s}} \nonumber
  891. \end{equation}
  892.  
  893. \end{columns}
  894.  
  895. }
  896.  
  897. \end{minipage}
  898. \vspace*{2.1cm}
  899. \end{frame}
  900. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  901. \begin{frame}{Transversity amplitudes }
  902. {~}
  903. \begin{minipage}{\textwidth}
  904.  
  905. $\color{JungleGreen}{\Rrightarrow}$ One can link the angular observables to transversity amplitudes
  906. {\tiny{
  907. \eqa{
  908. J_{1s} & = & \frac{(2+\beta_\ell^2)}{4} \left[|\apeL|^2 + |\apaL|^2 +|\apeR|^2 + |\apaR|^2 \right]
  909. + \frac{4 m_\ell^2}{q^2} \re\left(\apeL\apeR^* + \apaL\apaR^*\right)\,,\nn\\[1mm]
  910. %
  911. J_{1c} & = & |\azeL|^2 +|\azeR|^2 + \frac{4m_\ell^2}{q^2} \left[|A_t|^2 + 2\re(\azeL^{}\azeR^*) \right] + \beta_\ell^2\, |A_S|^2 \,,\nn\\[1mm]
  912. %
  913. J_{2s} & = & \frac{ \beta_\ell^2}{4}\left[ |\apeL|^2+ |\apaL|^2 + |\apeR|^2+ |\apaR|^2\right],
  914. \hspace{0.92cm} J_{2c} = - \beta_\ell^2\left[|\azeL|^2 + |\azeR|^2 \right]\,,\nn\\[1mm]
  915. %
  916. J_3 & = & \frac{1}{2}\beta_\ell^2\left[ |\apeL|^2 - |\apaL|^2 + |\apeR|^2 - |\apaR|^2\right],
  917. \qquad J_4 = \frac{1}{\sqrt{2}}\beta_\ell^2\left[\re (\azeL\apaL^* + \azeR\apaR^* )\right],\nn \\[1mm]
  918. %
  919. J_5 & = & \sqrt{2}\beta_\ell\,\Big[\re(\azeL\apeL^* - \azeR\apeR^* ) - \frac{m_\ell}{\sqrt{q^2}}\,
  920. \re(\apaL A_S^*+ \apaR^* A_S) \Big]\,,\nn\\[1mm]
  921. %
  922. J_{6s} & = & 2\beta_\ell\left[\re (\apaL\apeL^* - \apaR\apeR^*) \right]\,,
  923. \hspace{2.25cm} J_{6c} = 4\beta_\ell\, \frac{m_\ell}{\sqrt{q^2}}\, \re (\azeL A_S^*+ \azeR^* A_S)\,,\nn\\[1mm]
  924. %
  925. J_7 & = & \sqrt{2} \beta_\ell\, \Big[\im (\azeL\apaL^* - \azeR\apaR^* ) +
  926. \frac{m_\ell}{\sqrt{q^2}}\, \im (\apeL A_S^* - \apeR^* A_S)) \Big]\,,\nn\\[1mm]
  927. %
  928. J_8 & = & \frac{1}{\sqrt{2}}\beta_\ell^2\left[\im(\azeL\apeL^* + \azeR\apeR^*)\right]\,,
  929. %
  930. \hspace{1.9cm} J_9 = \beta_\ell^2\left[\im (\apaL^{*}\apeL + \apaR^{*}\apeR)\right] \,,
  931. \label{Js}\nonumber}
  932. }}
  933.  
  934. \end{minipage}
  935. \vspace*{2.1cm}
  936. \end{frame}
  937.  
  938.  
  939.  
  940. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  941. \begin{frame}{Link to effective operators}
  942. {~}
  943. \begin{minipage}{\textwidth}
  944. $\color{JungleGreen}{\Rrightarrow}$ So here is where the magic happens. At leading order the amplitudes can be written as:
  945. {\tiny{
  946. \eqa{
  947. \apeLR &=&\sqrt{2} N m_B(1- \hat s)\bigg[ (\Ceff9 + \Cpeff9) \mp (\C{10} + \Cp{10})
  948. +\frac{2\hat{m}_b}{\hat s} (\Ceff7 + \Cpeff7) \bigg]\xi_{\bot}(E_{K^*}) \nn \\[2mm]
  949. \apaLR &=& -\sqrt{2} N m_B (1-\hat s)\bigg[(\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10})
  950. +\frac{2\hat{m}_b}{\hat s}(\Ceff7 - \Cpeff7) \bigg] \xi_{\bot}(E_{K^*}) \nn \\[2mm]
  951. \azeLR &=& -\frac{N m_B (1-\hat s)^2}{2 \hat{m}_{K^*} \sqrt{\hat s}} \bigg[ (\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10}) + 2\hat{m}_b (\Ceff7 - \Cpeff7) \bigg]\xi_{\|}(E_{K^*}),
  952. \label{LargeRecoilAs}\nonumber}
  953. }}
  954. where $\hat s = q^2 /m_B^2$, $\hat{m}_i = m_i/m_B$. The $\xi_{\|,\bot }$ are the form factors. \\
  955. \pause
  956. $\color{JungleGreen}{\Rrightarrow}$ Now we can construct observables that cancel the $\xi$ form factors at leading order:
  957. \eq{P_5^{\prime} = \dfrac{J_5+\bar{J}_5}{2\sqrt{-(J_2^c+\bar{J}_2^c)(J_2^s+\bar{J}_2^s)} }\nonumber
  958. }
  959.  
  960.  
  961. \end{minipage}
  962. \vspace*{2.1cm}
  963. \end{frame}
  964. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  965. \begin{frame}
  966. \begin{center}
  967. \begin{Huge}
  968. LHCb measurement of $\PBd \to \PKstar \Pmu \Pmu$
  969. \end{Huge}
  970. \end{center}
  971.  
  972.  
  973.  
  974.  
  975. \end{frame}
  976.  
  977.  
  978. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  979. \begin{frame}{LHCbs $\PB \to \PKstar \Pmuon \APmuon$, Selection}
  980. {~}
  981. \begin{minipage}{\textwidth}
  982. \begin{footnotesize}
  983. \begin{columns}
  984. \column{0.2in}
  985. {~}
  986. \column{2in}
  987. \ARROW Trigger
  988. \begin{itemize}
  989. \item Muon trigger.
  990. \item Topological trigger.
  991. \end{itemize}
  992. \ARROW Good modelling with MC. \\
  993. \ARROW Selection:
  994. \begin{itemize}
  995. \item As loose as possible.
  996. \item Based on the $\PBzero$ vertex quality, impact parameters, loose Particle identification for the hadrons.
  997. \item The variables were chosen in a way we are sure the are correctly modelled in MC.
  998. \end{itemize}
  999. \column{2.8in}
  1000.  
  1001. \includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_pt}.pdf}\\
  1002. \includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_costhetal}.pdf}
  1003. \end{columns}
  1004.  
  1005.  
  1006.  
  1007. \end{footnotesize}
  1008.  
  1009.  
  1010.  
  1011. \end{minipage}
  1012. \vspace*{2.1cm}
  1013. \end{frame}
  1014.  
  1015. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1016. \begin{frame}{Peaking backgrounds}
  1017. {~}
  1018. \begin{minipage}{\textwidth}
  1019. \begin{footnotesize}
  1020. \ARROW A number of peaking backgrounds that can mistaken as your signal.\\
  1021. \ARROW There where a specially designed vetoes to fight each of them.
  1022. \begin{center}
  1023. \begin{tiny}
  1024. \hspace{-1cm}\begin{tabular}{ r | c c | c c }
  1025. \hline
  1026. & \multicolumn{2}{c|}{after preselection, before vetoes} & \multicolumn{2}{c }{after vetoes and selection}\\
  1027. Channel & Estimated events & \% signal & Estimated events & \% signal \\
  1028. \hline
  1029. \hline
  1030. $\Lambda_b \to \Lambda^{\ast}(1520)^{0} \mu\mu$ &$ (1.0\pm0.5)\times10^3 $&$ 19\pm8 $&$ 51\pm25 $&$ 1.0\pm0.4$\\
  1031. $\Lambda_b \to {\rm p } \PK \mu\mu$ &$ (1.0\pm0.5)\times10^2 $&$ 1.9\pm0.8 $&$ 5.7\pm2.8 $&$ 0.11\pm0.05$ \\
  1032. $\PB \to \PKplus \mu \mu$ &$ 28\pm7 $&$ 0.55\pm0.06 $&$ 1.6\pm0.5 $&$ 0.031\pm0.006$\\
  1033. $\PBs \to \Pphi \mu \mu$ &$ (3.2\pm1.3)\times10^2 $&$ 6.2\pm2.1 $&$ 17\pm7 $&$ 0.33\pm0.12$\\
  1034. signal swaps &$ (3.6\pm0.9)\times10^2 $&$ 6.9\pm0.6 $&$ 33\pm9 $&$ 0.64\pm0.06$ \\
  1035. $\PB \to \PKstar \PJpsi$ swaps &$ (1.3\pm0.4)\times10^2 $&$ 2.6\pm0.4 $&$ 2.7\pm2.8 $&$ 0.05\pm0.05$ \\
  1036. \hline
  1037. \end{tabular}
  1038. \end{tiny}
  1039. \includegraphics[angle=-90,width=0.49\textwidth]{{images/h_Bd_Kstmm_vetoes}.pdf}
  1040. \includegraphics[angle=-90,width=0.49\textwidth]{{h_Lb_L1520mm_vetoes}.pdf}
  1041.  
  1042. \end{center}
  1043.  
  1044.  
  1045.  
  1046.  
  1047. \end{footnotesize}
  1048.  
  1049.  
  1050.  
  1051. \end{minipage}
  1052. \vspace*{2.1cm}
  1053. \end{frame}
  1054.  
  1055. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1056. \begin{frame}{Multivariate simulation}
  1057. {~}
  1058. \begin{minipage}{\textwidth}
  1059. \begin{columns}
  1060.  
  1061. \column{0.5\textwidth}
  1062. \begin{itemize}
  1063. \begin{footnotesize}
  1064. \item PID, kinematics and isolation variables used in a Boosted Decision Tree (BDT) to discriminate signal and background.
  1065. \item BDT with k-Folding technique.
  1066. \item Completely data driven.
  1067. \end{footnotesize}
  1068. \end{itemize}
  1069. \begin{center}
  1070. \includegraphics[width=0.70\textwidth]{images/Chopping_Distrib.pdf}
  1071. \end{center}
  1072.  
  1073. \column{0.5\textwidth}
  1074.  
  1075. \includegraphics[angle=-90,width=0.82\textwidth]{images/Fig1.pdf} \\
  1076. \includegraphics[width=0.88\textwidth]{images/fold.png}
  1077.  
  1078. \end{columns}
  1079.  
  1080.  
  1081.  
  1082. \end{minipage}
  1083. \vspace*{2.1cm}
  1084. \end{frame}
  1085.  
  1086.  
  1087. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1088. \begin{frame}{Multivariate simulation, efficiency}
  1089. {~}
  1090.  
  1091. \begin{minipage}{\textwidth}
  1092. \begin{footnotesize}
  1093.  
  1094. \ARROW BDT was also checked in order not to bias our angular distribution:
  1095. \begin{center}
  1096. \includegraphics[angle=-90,width=0.8\textwidth]{images/BDT_Eff_Comp.pdf}
  1097. \end{center}
  1098. \ARROW The BDT has small impact on our angular observables. We will correct for these effects later on.
  1099.  
  1100. \end{footnotesize}
  1101. \end{minipage}
  1102. \vspace*{2.1cm}
  1103. \end{frame}
  1104. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1105.  
  1106.  
  1107. \begin{frame}{Mass modelling}
  1108. {~}
  1109. \begin{minipage}{\textwidth}
  1110. \begin{tiny}
  1111. \begin{columns}
  1112. \column{0.1in}
  1113. {~}
  1114. \column{2.5in}
  1115. \ARROW The signal is modelled by a sum of two Crystal-Ball functions with common mean.\\
  1116. \ARROW The background is a single exponential.\\
  1117. \ARROW The base parameters are obtained from the proxy channel: $\PBd \to \PJpsi (\mu\mu) \PKstar$.\\
  1118. \ARROW All the parameters are fixed in the signal pdf.\\
  1119. \ARROW Scaling factors for resolution are determined from MC.\\
  1120. \ARROW In fitting the rare mode only the signal, background yield and the slope of the exponential is left floating.\\
  1121. \begin{center}
  1122. \includegraphics[angle=-90,width=0.8\textwidth]{images/msignal.pdf}\\
  1123.  
  1124. \end{center}
  1125. \ARROW We found $624\pm30$ candidates in the most interesting $\left[1.1,6.0\right]~\GeV^2/c^4$ region \\ and $2398 \pm 57$ in the full range $\left[ 1.1, 19.\right]~\GeV^2/c^4$.
  1126. \column{2.5in}
  1127. \includegraphics[angle=-90,width=0.95\textwidth]{{images/FitJpsiKstar_withBDT_withoutPartially}.pdf}\\
  1128. \includegraphics[angle=-90,width=0.95\textwidth]{{images/Scaling_factor}.pdf}\\
  1129. \ARROW The S-wave fraction is extracted using a \texttt{LASS} model.
  1130. \end{columns}
  1131.  
  1132. \end{tiny}
  1133. \end{minipage}
  1134. \vspace*{2.1cm}
  1135. \end{frame}
  1136. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1137. \begin{frame}{Monte Carlo corrections}
  1138. {~}
  1139. \begin{minipage}{\textwidth}
  1140. \begin{footnotesize}
  1141. \ARROW No Monte Carlo simulation is perfect! One needs to correct for remaining differences.\\
  1142. \ARROW We reweighted our $\PBd \to \PKstar \mu \mu$ Monte Carlo accordingly to differences between the $\PBd \to \PKstar \PJpsi$ in data (Splot) and Monte Carlo.
  1143. \only<1>{
  1144. \begin{center}
  1145. \includegraphics[angle=-90,width=0.38\textwidth]{images/pt.pdf}
  1146. \includegraphics[angle=-90,width=0.38\textwidth]{images/vertex.pdf}\\
  1147. \includegraphics[angle=-90,width=0.38\textwidth]{images/nTracks.pdf}
  1148. \end{center}
  1149. }
  1150. \only<2>{
  1151. \begin{center}
  1152. \includegraphics[angle=-90,width=0.38\textwidth]{images/eta_logy.pdf}
  1153. \includegraphics[angle=-90,width=0.38\textwidth]{images/B0_p.pdf} \\
  1154. \includegraphics[angle=-90,width=0.38\textwidth]{{images/bdt_data_mc_nominalMkpi}.pdf}
  1155. \end{center}
  1156. }
  1157.  
  1158. \end{footnotesize}
  1159. \end{minipage}
  1160. \vspace*{2.1cm}
  1161. \end{frame}
  1162.  
  1163.  
  1164. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1165.  
  1166.  
  1167.  
  1168.  
  1169.  
  1170.  
  1171.  
  1172. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1173. \begin{frame}{Detector acceptance}
  1174. {~}
  1175. \begin{minipage}{\textwidth}
  1176. \begin{footnotesize}
  1177.  
  1178. \begin{columns}
  1179.  
  1180. \column{0.6\textwidth}
  1181. \begin{itemize}
  1182. \item Detector distorts our angular distribution.
  1183. \item We need to model this effect.
  1184. \item 4D function is used:
  1185. \begin{align*}
  1186. \epsilon (\cos \thetal, \cos \thetak, \phi, q^2) = \\\sum_{ijkl} P_i(\cos \thetal) P_j(\cos \thetak ) P_k(\phi) P_l(q^2),
  1187. \end{align*}
  1188. where $P_i$ is the Legendre polynomial of order $i$.
  1189. \item We use up to $4^{th}, 5^{th}, 6^{th}, 5^{th}$ order for the $\cos \thetal, \cos \thetak, \phi, q^2$.
  1190. \item The coefficients were determined using Method of Moments, with a huge simulation sample.
  1191. \item The simulation was done assuming a flat phase space and reweighing the $q^2$ distribution to make is flat.
  1192. \item To make this work the $q^2$ distribution needs to be reweighted to be flat.
  1193. \end{itemize}
  1194. %\includegraphics[width=0.75\textwidth]{images/q2PHSP.png}
  1195.  
  1196.  
  1197.  
  1198. \column{0.4\textwidth}
  1199. \only<1>{
  1200. \includegraphics[width=0.99\textwidth]{images/q2PHSP.png}\\
  1201. \includegraphics[width=0.99\textwidth]{images/q2PHSPw.png}
  1202. }
  1203.  
  1204. \only<2>{
  1205. \includegraphics[width=0.99\textwidth]{images/det.png}
  1206. }
  1207. \end{columns}
  1208.  
  1209.  
  1210. \end{footnotesize}
  1211. \end{minipage}
  1212. \vspace*{2.1cm}
  1213. \end{frame}
  1214.  
  1215.  
  1216. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1217.  
  1218.  
  1219. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1220. \begin{frame}{Control channel}
  1221. {~}
  1222. \begin{minipage}{\textwidth}
  1223. \begin{footnotesize}
  1224. \begin{itemize}
  1225. \item We tested our unfolding procedure on $\PB \to \PJpsi \PKstar$.
  1226. \item The result is in perfect agreement with other experiments and our different analysis of this decay.
  1227. \end{itemize}
  1228. \end{footnotesize}
  1229. \begin{center}
  1230. \includegraphics[angle=-90,width=0.4\textwidth]{images/mlogjpsi.pdf}
  1231. \includegraphics[angle=-90,width=0.4\textwidth]{images/mkpijpsi.pdf}\\
  1232. \includegraphics[width=0.99\textwidth]{images/angles3.png}
  1233. \end{center}
  1234.  
  1235.  
  1236. \end{minipage}
  1237. \vspace*{2.1cm}
  1238. \end{frame}
  1239.  
  1240.  
  1241. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1242. \begin{frame}{The columns of New Physics}
  1243. {~}
  1244. \begin{minipage}{\textwidth}
  1245. \begin{center}
  1246. \includegraphics[width=0.94\textwidth]{images/columns.png}
  1247.  
  1248. \end{center}
  1249.  
  1250.  
  1251. \end{minipage}
  1252. \vspace*{2.1cm}
  1253. \end{frame}
  1254.  
  1255.  
  1256.  
  1257. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1258. \begin{frame}{The columns of New Physics}
  1259. {~}
  1260. \begin{minipage}{\textwidth}
  1261. \begin{enumerate}
  1262. \item Maximum likelihood fit:
  1263. \begin{itemize}
  1264. \item The most standard way of obtaining the parameters.
  1265. \item Suffers from convergence problems, under coverages, etc. in low statistics.
  1266. \end{itemize}
  1267. \item Method of moments:
  1268. \begin{itemize}
  1269. \item Less precise then the likelihood estimator ($10-15\%$ larger uncertainties).
  1270. \item Does not suffer from the problems of likelihood fit.
  1271. \end{itemize}
  1272. \item Amplitude fit:
  1273. \begin{itemize}
  1274. \item Incorporates all the physical symmetries inside the amplitudes! The most precise estimator.
  1275. \item Has theoretical assumptions inside!
  1276. \end{itemize}
  1277. \end{enumerate}
  1278.  
  1279. \end{minipage}
  1280. \vspace*{2.1cm}
  1281. \end{frame}
  1282.  
  1283.  
  1284. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1285.  
  1286. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1287. \begin{frame}{Maximum likelihood fit - Results}
  1288. {~}
  1289. \begin{footnotesize}
  1290.  
  1291. \begin{minipage}{\textwidth}
  1292. \ARROW In the maximum likelihood fit one could weight the events accordingly to the $\dfrac{1}{\varepsilon(\cos \thetal, \cos \thetak, \phi, q^2)}$\\
  1293. \ARROW Better alternative is to put the efficiency into the maximum likelihood fit itself:
  1294. \begin{align*}
  1295. \mathcal{L}=\prod_{i=1}^N \epsilon_i(\Omega_i, q_i^2) \mathcal{P}(\Omega_i, q_i^2) / \int \epsilon(\Omega, q^2) \mathcal{P}(\Omega, q^2) d\Omega dq^2
  1296. \end{align*}
  1297. \ARROW Only the relative weights matters!\\
  1298. \ARROW The Procedure was commissioned with TOY MC study.\\
  1299. \ARROW Use Feldmann-Cousins to determine the uncertainties. \\
  1300. \ARROW Angular background component is modelled with $2^{\rm nd }$ order Chebyshev polynomials, which was tested on the side-bands.\\
  1301. \ARROW S-wave component treated as nuisance parameter.\\
  1302. \includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_Afb3}.pdf}
  1303. \includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P11}.pdf}
  1304. \includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P57}.pdf}
  1305.  
  1306. \end{minipage}
  1307. \end{footnotesize}
  1308. \vspace*{2.1cm}
  1309. \end{frame}
  1310.  
  1311. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1312. \begin{frame}{Maximum likelihood fit - Results}
  1313. {~}
  1314. \begin{minipage}{\textwidth}
  1315. \begin{center}
  1316. \only<1>{
  1317. \includegraphics[angle=-90,width=0.49\textwidth]{images/FLPad.pdf}
  1318. \includegraphics[angle=-90,width=0.49\textwidth]{images/S3Pad.pdf}\\
  1319. \includegraphics[angle=-90,width=0.49\textwidth]{images/S4Pad.pdf}
  1320. \includegraphics[angle=-90,width=0.49\textwidth]{images/S5Pad.pdf}
  1321. }
  1322. \only<2>{
  1323. \includegraphics[angle=-90,width=0.49\textwidth]{images/AFBPad.pdf}
  1324. \includegraphics[angle=-90,width=0.49\textwidth]{images/S7Pad.pdf}\\
  1325. \includegraphics[angle=-90,width=0.49\textwidth]{images/S8Pad.pdf}
  1326. \includegraphics[angle=-90,width=0.49\textwidth]{images/S9Pad.pdf}
  1327. }
  1328.  
  1329.  
  1330. \end{center}
  1331.  
  1332. \end{minipage}
  1333. \vspace*{2.1cm}
  1334. \end{frame}
  1335.  
  1336.  
  1337.  
  1338.  
  1339.  
  1340.  
  1341.  
  1342.  
  1343. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1344. \begin{frame}{Maximum likelihood fit - Results}
  1345. \begin{minipage}{\textwidth}
  1346. \begin{center}
  1347. \includegraphics[angle=-90,width=0.65\textwidth]{images/P5pPadOverlay.pdf}\\
  1348. \end{center}
  1349.  
  1350. \begin{itemize}
  1351. \item Tension with $3~\invfb$ gets confirmed!
  1352. \item two bins both deviate by $2.8~\sigma$ from SM prediction.
  1353. \item Result compatible with previous result.
  1354. \end{itemize}
  1355.  
  1356.  
  1357. \end{minipage}
  1358. \vspace*{2.1cm}
  1359. \end{frame}
  1360.  
  1361.  
  1362.  
  1363.  
  1364.  
  1365.  
  1366. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1367.  
  1368.  
  1369.  
  1370.  
  1371. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1372. \begin{frame}{Method of moments}
  1373. {~}
  1374. \begin{footnotesize}
  1375. \begin{minipage}{\textwidth}
  1376. \ARROW See {\color{blue}{\href{http://arxiv.org/abs/1503.04100}{Phys.Rev.D91(2015)114012}}}, F.Beaujean , M.Chrzaszcz, N.Serra, D. van Dyk for details.\\
  1377. \ARROW The idea behind Method of Moments is simple: Use orthogonality of spherical harmonics, $f_j(\overrightarrow{\Omega})$ to solve for coefficients within a $q^2$ bin:
  1378. \begin{align*}
  1379. \int f_i(\overrightarrow{\Omega}) f_j(\overrightarrow{\Omega}) = \delta_{ij}
  1380. \end{align*}
  1381. \begin{align*}
  1382. M_i = \int \left( \dfrac{1}{d(\Gamma+ \bar{\Gamma})/dq^2} \right) \dfrac{d^3(\Gamma+\bar{\Gamma})}{d \overrightarrow{\Omega}} f_i(\overrightarrow{\Omega})d \Omega
  1383. \end{align*}
  1384. \ARROW Don’t have true angular distribution but we ''sample'' it with our data.\\
  1385. \ARROW Therefore: $\int \to \sum$ and $M_i \to \widehat{M}_i$
  1386. \begin{align*}
  1387. \hat{M}_i=\dfrac{1}{\sum_e \omega_e} \sum_e \omega_e f_i(\overrightarrow{\Omega}_e)
  1388. \end{align*}
  1389. \ARROW The weight $\omega$ accounts for the efficiency. Again the normalization of weights does not matter.
  1390.  
  1391.  
  1392. \end{minipage}
  1393. \end{footnotesize}
  1394. \vspace*{2.1cm}
  1395. \end{frame}
  1396.  
  1397.  
  1398.  
  1399. \begin{frame}{Method of moments - results}
  1400. {~}
  1401. \begin{footnotesize}
  1402. \begin{minipage}{\textwidth}
  1403. \only<3>
  1404. {
  1405. \ARROW Method of Moments allowed us to measure for the first time a new observable:
  1406. }
  1407. \begin{center}
  1408. \only<1>{
  1409. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_FLPad.pdf}
  1410. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S3Pad.pdf}\\
  1411. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S4Pad.pdf}
  1412. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S5Pad.pdf}
  1413. }
  1414. \only<2>{
  1415. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_AFBPad.pdf}
  1416. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S7Pad.pdf}\\
  1417. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S8Pad.pdf}
  1418. \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S9Pad.pdf}
  1419. }
  1420. \only<3>{
  1421. \includegraphics[angle=-90,width=0.75\textwidth]{images/S6cPad.pdf}
  1422. }
  1423.  
  1424. \end{center}
  1425. \end{minipage}
  1426. \end{footnotesize}
  1427. \vspace*{2.1cm}
  1428. \end{frame}
  1429.  
  1430.  
  1431.  
  1432.  
  1433.  
  1434. \begin{frame}{Amplitudes method}
  1435. {~}
  1436. \begin{footnotesize}
  1437. \begin{minipage}{\textwidth}
  1438.  
  1439. \ARROW Fit for amplitudes as (continuous) functions of $q^2$ in the region: $q^2 \in \left[ 1.1. 6.0 \right]~\GeV^2/c^4$.\\
  1440. \ARROW Needs some Ansatz:
  1441. \begin{align*}
  1442. A(q^2) = \alpha + \beta q^2+ \dfrac{\gamma}{q^2}
  1443. \end{align*}
  1444. \ARROW The assumption is tested extensively with toys.\\
  1445. \ARROW Set of 3 complex parameters $ \alpha, \beta, \gamma $ per vector amplitude:\begin{itemize}
  1446. \item {\color{Magenta}{$L, ~R$}}, {\color{Cerulean}{$0 ,~\| ,~\bot$}}, {\color{PineGreen}{$\Re ,~\Im$}} $\rightarrowtail$~~ $3 \times {\color{PineGreen}{2}} \times {\color{Cerulean}{3}} \times {\color{Magenta}{2}} = 36$ DoF.
  1447. \item Scalar amplitudes: $+4$ DoF.
  1448. \item Symmetries of the amplitudes reduces the total budget to: $28$.
  1449. \end{itemize}
  1450. \ARROW The technique is described in \href{http://arxiv.org/pdf/1504.00574v2.pdf}{\color{blue}{JHEP06(2015)084}}.\\
  1451. \ARROW Allows to build the observables as continuous functions of $q^2$:
  1452. \begin{itemize}
  1453. \item At current point the method is limited by statistics.
  1454. \item In the future the power of this method will increase.
  1455. \end{itemize}
  1456. \ARROW Allows to measure the zero-crossing points for free and with smaller errors than previous methods.
  1457. \end{minipage}
  1458. \end{footnotesize}
  1459. \vspace*{2.1cm}
  1460. \end{frame}
  1461.  
  1462.  
  1463.  
  1464. \begin{frame}{Amplitudes - results}
  1465. {~}
  1466. \begin{footnotesize}
  1467. \begin{minipage}{\textwidth}
  1468. \begin{center}
  1469. \begin{columns}
  1470. \column{0.45\textwidth}
  1471. \includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_AFBOverlay}.pdf}\\
  1472. \includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S4Overlay}.pdf}
  1473.  
  1474. \column{0.45\textwidth}
  1475. \includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S5Overlay}.pdf}\\
  1476. {~}\\{~}\\{~}\\{~}\\
  1477. \begin{large}
  1478. Zero crossing points:
  1479. \end{large}
  1480. \begin{align*}
  1481. q_0(S_4) & <2.65 & {\rm{~at~}} & 95\% ~CL \\
  1482. q_0(S_5) & \in \left[ 2.49,3.95 \right] & {\rm{~at~}} & 68\% ~CL \\
  1483. q_0(A_{FB}) & \in \left[ 3.40, 4.87 \right] & {\rm{~at~}} & 68\% ~CL
  1484. \end{align*}
  1485.  
  1486.  
  1487. \end{columns}
  1488. \end{center}
  1489.  
  1490. \end{minipage}
  1491. \end{footnotesize}
  1492. \vspace*{2.1cm}
  1493. \end{frame}
  1494.  
  1495.  
  1496.  
  1497.  
  1498. \begin{frame}{Compatibility with SM}
  1499. {~}
  1500.  
  1501. \begin{minipage}{\textwidth}
  1502.  
  1503. \begin{columns}
  1504. \column{0.1in}
  1505. {~}
  1506. \column{2in}
  1507. \ARROW Use \texttt{EOS} software package to test compatibility with SM.\\
  1508. \ARROW Perform the $\chi^2$ fit to the measured:
  1509. \begin{center}
  1510. \begin{align*}
  1511. F_L, A_{FB}, S_{3,..., 9} .
  1512. \end{align*}
  1513. \end{center}
  1514. \ARROW Float a vector coupling: $\Re(C_9)$.\\
  1515. \ARROW Best fit is found to be $3.4~\sigma$ away from the SM.
  1516.  
  1517.  
  1518. \column{3in}
  1519. \begin{align*}
  1520. \Delta \Re (C_9) \equiv \Re(C_9)^{{\rm fit}} - \Re(C_9)^{{\rm SM}} = -1.03
  1521. \end{align*}
  1522. \includegraphics[angle=-90,width=0.95\textwidth]{images/wilsonchi2.pdf}
  1523. \end{columns}
  1524.  
  1525.  
  1526.  
  1527. \end{minipage}
  1528.  
  1529. \vspace*{2.1cm}
  1530. \end{frame}
  1531.  
  1532.  
  1533.  
  1534.  
  1535. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1536. \begin{frame}
  1537. \begin{center}
  1538. \begin{Huge}
  1539. Other related LHCb measurements.
  1540.  
  1541. \end{Huge}
  1542. \end{center}
  1543.  
  1544.  
  1545.  
  1546.  
  1547. \end{frame}
  1548.  
  1549.  
  1550.  
  1551.  
  1552.  
  1553.  
  1554.  
  1555.  
  1556.  
  1557.  
  1558.  
  1559.  
  1560.  
  1561. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1562. \begin{frame}{Branching fraction measurements of $\PB \to \PKstar^{\pm} \Pmu \Pmu$}
  1563. {~}
  1564. \includegraphics[width=0.5\textwidth]{images/ksmumu_BF.png}
  1565. \includegraphics[width=0.5\textwidth]{images/kmumu_BF.png}
  1566.  
  1567. \begin{center}
  1568. \begin{columns}
  1569.  
  1570. \column{0.4\textwidth}
  1571. \begin{itemize}
  1572. \item Despite large theoretical errors the results are consistently smaller than SM prediction.
  1573. \end{itemize}
  1574. \column{0.6\textwidth}
  1575. \includegraphics[width=0.87\textwidth]{images/bukst_BF.png}
  1576.  
  1577.  
  1578. \end{columns}
  1579.  
  1580.  
  1581.  
  1582.  
  1583.  
  1584.  
  1585.  
  1586. \end{center}
  1587. \vspace*{2.1cm}
  1588. \end{frame}
  1589.  
  1590. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1591. \begin{frame}{Branching fraction measurements of $\PBs \to \Pphi \Pmu \Pmu$}
  1592. {~}
  1593. \begin{minipage}{\textwidth}
  1594. \begin{center}
  1595. \includegraphics[width=0.65\textwidth]{images/bs2phipi.png}\\
  1596. \end{center}
  1597.  
  1598. \begin{itemize}
  1599. \item Recent LHCb measurement [JHEPP09 (2015) 179].
  1600. \item Suppressed by $\frac{f_s}{f_d}$.
  1601. \item Cleaner because of narrow $\Pphi$ resonance.
  1602. \item $3.3~\sigma$ deviation in SM in the $1-6\GeV^2$ bin.
  1603. \end{itemize}
  1604.  
  1605.  
  1606. \end{minipage}
  1607. \vspace*{2.1cm}
  1608. \end{frame}
  1609.  
  1610.  
  1611. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1612. \begin{frame}{Branching fraction measurements of $\Lambda_b \to \Lambda \Pmu \Pmu$}
  1613. {~}
  1614. \begin{minipage}{\textwidth}
  1615.  
  1616. \begin{center}
  1617. \only<1>{
  1618. \includegraphics[width=0.65\textwidth]{images/Lb_BR.png}
  1619. }
  1620. \only<2>{
  1621. \includegraphics[width=0.45\textwidth]{images/Lblow.png}
  1622. \includegraphics[width=0.45\textwidth]{images/Lbhigh.png}
  1623.  
  1624. }
  1625.  
  1626.  
  1627. \end{center}
  1628.  
  1629.  
  1630. \begin{itemize}
  1631. \item This years LHCb measurement [JHEP 06 (2015) 115]].
  1632. \item In total $\sim 300$ candidates in data set.
  1633. \item Decay not present in the low $q^2$.
  1634.  
  1635. \end{itemize}
  1636.  
  1637.  
  1638.  
  1639. \end{minipage}
  1640. \vspace*{2.1cm}
  1641. \end{frame}
  1642.  
  1643.  
  1644. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1645.  
  1646. \begin{frame}{Angular analysis of $\Lambda_b \to \Lambda \Pmu \Pmu$}
  1647. {~}
  1648. \begin{minipage}{\textwidth}
  1649.  
  1650. \begin{itemize}
  1651. \item For the bins in which we have $>3~\sigma$ significance the forward backward asymmetry for the hadronic and leptonic system.
  1652. \end{itemize}
  1653. \begin{center}
  1654. \includegraphics[width=0.9\textwidth]{{images/AFB_Lb}.png}
  1655. \end{center}
  1656. \begin{itemize}
  1657. \item $A_{FB}^H$ is in good agreement with SM.
  1658. \item $A_{FB}^{\ell}$ always in above SM prediction.
  1659. \end{itemize}
  1660.  
  1661.  
  1662. \end{minipage}
  1663. \vspace*{2.1cm}
  1664. \end{frame}
  1665.  
  1666.  
  1667.  
  1668.  
  1669. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1670. \begin{frame}{Lepton universality test}
  1671. {~}
  1672. \begin{minipage}{\textwidth}
  1673. \begin{columns}
  1674. \column{3.0in}
  1675. \begin{itemize}
  1676. \item If we attribute the deviations to NP, is it Lepton Universal?
  1677. \includegraphics[width=0.9\textwidth]{images/uni2.png}
  1678. \item Challenging analysis due to bremsstrahlung.
  1679. \item Migration of events modeled by MC.
  1680. \item Correct for bremsstrahlung.
  1681. \item Take double ratio with $\PBplus \to \PJpsi \PKplus$ to cancel systematics.
  1682. \item In $3\invfb$, LHCb measures $R_K=0.745^{+0.090}_{-0.074}(stat.)^{+0.036}_{-0.036}(syst.)$
  1683. \item Consistent with SM at $2.6\sigma$.
  1684.  
  1685. \end{itemize}
  1686. \column{2.0in}
  1687. \includegraphics[width=0.99\textwidth]{images/RK.png}\\
  1688. \begin{itemize}
  1689. \item \href{http://arxiv.org/abs/1406.6482}{Phys. Rev. Lett. 113, 151601 (2014)}
  1690. \end{itemize}
  1691. \end{columns}
  1692.  
  1693.  
  1694.  
  1695. \end{minipage}
  1696. \vspace*{2.1cm}
  1697. \end{frame}
  1698.  
  1699.  
  1700. \begin{frame}\frametitle{There is more!}
  1701. %https://indico.cern.ch/event/580620/
  1702. \ARROW We followed this path...\\
  1703. \ARROW We measured the ratio:
  1704. \begin{equation*}
  1705. R_{\PKstar}= \frac{\mathcal{B}( \PB \to \PKstar \Pmu \Pmu)}{\mathcal{B}( \PB \to \PKstar \Pe \Pe)}
  1706. \end{equation*}
  1707. \pause
  1708.  
  1709. \begin{columns}
  1710. \column{0.4\textwidth}
  1711. \ARROW Measurement performed in two $q^2$ bins. \\
  1712. \ARROW Normalized in double ratio to $\PB \to \PKstar \PJpsi$.\\
  1713. \includegraphics[width=0.95\textwidth]{images/plot.png}
  1714.  
  1715.  
  1716. \column{0.6\textwidth}
  1717. \begin{center}
  1718. \includegraphics[width=0.95\textwidth]{images/RKstar.png}
  1719. \end{center}
  1720.  
  1721. \end{columns}
  1722.  
  1723.  
  1724.  
  1725. \end{frame}
  1726.  
  1727.  
  1728.  
  1729. \begin{frame}
  1730. \begin{center}
  1731. \begin{Huge}
  1732. Global analysis of $\Pbeauty \to \Pstrange \ell \ell$ measurements
  1733. \end{Huge}
  1734. \end{center}
  1735.  
  1736.  
  1737.  
  1738.  
  1739. \end{frame}
  1740.  
  1741.  
  1742.  
  1743. \begin{frame}{Link the observables}
  1744. \begin{footnotesize}
  1745.  
  1746. \ARROW Fits prepare by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}, \href{https://arxiv.org/abs/1704.05340}{\color{blue}{arXiv::1704.05340}}
  1747.  
  1748. \begin{itemize}
  1749.  
  1750. \item Inclusive
  1751.  
  1752. \begin{itemize}
  1753. \item $B\to X_s\gamma$ {\color{gray}($BR$)
  1754. .......................................................... } {\color{red} $\C7^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
  1755. \item $B\to X_s\ell^+\ell^-$ {\color{gray}($dBR/dq^2$)
  1756. ............................................ } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
  1757. \end{itemize}
  1758.  
  1759. \item Exclusive leptonic
  1760.  
  1761. \begin{itemize}
  1762. \item $B_s\to \ell^+\ell^-$ {\color{gray}($BR$)
  1763. ........................................................ } {\color{red} $\C{10}^{(\prime)}$}
  1764. \end{itemize}
  1765.  
  1766. \item Exclusive radiative/semileptonic
  1767. \begin{itemize}
  1768. \item $B\to K^*\gamma$ {\color{gray}($BR$, $S$, $A_I$)
  1769. ................................................ } {\color{red} $\C7^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
  1770.  
  1771. \item $B\to K\ell^+\ell^-$ {\color{gray}($dBR/dq^2$)
  1772. .............................................. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
  1773.  
  1774. \item $\bf \color{Red} B\to K^*\ell^+\ell^-$ {\color{gray}($dBR/dq^2$, {\bf Optimized Angular Obs.})
  1775. .. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
  1776.  
  1777. \item $B_s\to \phi \ell^+\ell^-$ {\color{gray}($dBR/dq^2$, Angular Observables)
  1778. .............. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
  1779.  
  1780. \item $\Lambda_b\to \Lambda\ell^+\ell^-$ {\color{gray}(None so far)}
  1781. \item etc.
  1782. \end{itemize}
  1783.  
  1784.  
  1785.  
  1786. \end{itemize}
  1787. \end{footnotesize}
  1788.  
  1789. \end{frame}
  1790.  
  1791. \frame{ \frametitle{Statistic details}
  1792.  
  1793. \begin{footnotesize}
  1794.  
  1795. \ARROW Frequentist approach:
  1796. \medskip
  1797.  
  1798. $$\chi^2(C_i) = [O_\text{exp}- O_\text{th}(C_i)]_j \, [Cov^{-1}]_{jk}\, [O_\text{exp}- O_\text{th}(C_i)]_k$$
  1799.  
  1800.  
  1801. \begin{itemize}
  1802. \item $\bf Cov = Cov^\text{exp} + Cov^\text{th}$. We have $Cov^\text{exp}$ for the first time
  1803. \item Calculate $Cov^\text{th}$: correlated multigaussian scan over all nuisance parameters
  1804. \item $Cov^\text{th}$ depends on $C_i$: Must check this dependence\\[5mm]
  1805. \end{itemize}
  1806. For the Fit:
  1807. \begin{itemize}
  1808. \item Minimise $\chi^2 \to \chi^2_\text{min} = \chi^2(C_i^0)\quad$ (Best Fit Point = $C_i^0$)
  1809. \item Confidence level regions: $\chi^2(C_i) - \chi^2_\text{min} < \Delta\chi_{\sigma,n}$
  1810. %\item Compute pulls by inversion of the above formula
  1811. \end{itemize}
  1812. \medskip
  1813. \ARROW The results from 1D scans:{~}\\{~}\\
  1814. \iffalse
  1815. \begin{tiny}
  1816. \begin{tabular}{crccc}
  1817. %\toprule[1.6pt]
  1818. Coefficient ${\cal C}_i^{NP}={\cal C}_i-{\cal C}_i^{SM}$ & Best fit & 1$\sigma$ & 3$\sigma$ & Pull$_{\rm SM}$ \\ \hspace{10mm} \\[5mm]
  1819. % \midrule
  1820. $\bf\cred\C9^{\rm NP}$ & $ -1.09 $ & $ [-1.29,-0.87] $ & $ [-1.67,-0.39] $ & $\,\,\,\,\,\,\bf 4.5
  1821. \cred \Leftarrow$ \hspace{5mm} \\[3mm]
  1822. $\C9^{\rm NP}=-\C{10}^{\rm NP}$ & $ -0.68 $ & $ [-0.85,-0.50] $ & $ [-1.22,-0.18] $ & \bf \quad 4.2
  1823. $\cred\Leftarrow$ \hspace{5mm} \\[3mm]
  1824. $\C9^{\rm NP}=-\C{9'}^{\rm NP}$ & $ -1.06 $ & $ [-1.25,-0.86] $ & $ [-1.60,-0.40] $ & \quad \quad \quad \,\,\quad 4.8
  1825. $\cred\Leftarrow$ (no $R_K$)\hspace{5mm} \\[3mm]
  1826.  
  1827. \hspace{5mm} \\[3mm]
  1828. % \bottomrule[1.6pt]
  1829. \end{tabular}
  1830. \end{tiny}
  1831.  
  1832. \fi
  1833. \includegraphics[width=0.99\textwidth]{images/table1.png}
  1834.  
  1835. \end{footnotesize}
  1836.  
  1837. }
  1838.  
  1839.  
  1840.  
  1841.  
  1842.  
  1843. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1844. \begin{frame}{Theory implications}
  1845. {~}
  1846. \begin{minipage}{\textwidth}
  1847.  
  1848. \begin{itemize}
  1849. \item The data can be explained by modifying the $C_9$ Wilson coefficient.
  1850. \item Overall there is around $4-5~\sigma$ discrepancy wrt. SM.
  1851. \end{itemize}
  1852. \includegraphics[width=0.9\textwidth]{images/C9.png}
  1853.  
  1854.  
  1855.  
  1856.  
  1857. \end{minipage}
  1858. \vspace*{2.1cm}
  1859. \end{frame}
  1860.  
  1861.  
  1862.  
  1863. \begin{frame}{2D scans}
  1864. {~}
  1865. \begin{footnotesize}
  1866.  
  1867. \begin{minipage}{\textwidth}
  1868. \begin{columns}
  1869. \begin{column}{0.5cm}
  1870.  
  1871.  
  1872. \end{column}
  1873. \begin{column}{17cm}
  1874.  
  1875. \renewcommand{\arraystretch}{1.4}
  1876. \setlength{\tabcolsep}{13pt}
  1877. \begin{tabular}{cccr}
  1878. \hline
  1879. Coefficient & Best Fit Point & Pull$_{\rm SM}$ \\ \hline
  1880.  
  1881. $(\C7^{\rm NP},\C9^{\rm NP})$ & $(-0.00,-1.07)$ & {\bf 4.1} \hspace{5mm} \\
  1882. $(\C9^{\rm NP},\C{10}^{\rm NP})$ & $(-1.08,0.33)$ & {\bf 4.3} \hspace{5mm} \\
  1883. $(\C9^{\rm NP},\C{7'}^{\rm NP})$ & $(-1.09,0.02)$ & {\bf 4.2} \hspace{5mm} \\
  1884. $(\C9^{\rm NP},\C{9'}^{\rm NP})$ & $(-1.12,0.77)$ & {\bf 4.5} \hspace{5mm} \\
  1885. $(\C9^{\rm NP},\C{10'}^{\rm NP})$ & $(-1.17,-0.35)$ & {\bf 4.5} \hspace{5mm} \\
  1886. $(\C{9}^{\rm NP}=-\C{9'}^{\rm NP},\C{10}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-1.15,0.34)$ & \!\!\!\!\!\!\!\!\!\!\! {\bf 4.7} \\
  1887. $(\C{9}^{\rm NP}=-\C{9'}^{\rm NP},\C{10}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-1.06,0.06)$ & {\bf 4.4} \hspace{5mm} \\
  1888. $(\C{9}^{\rm NP}=\C{9'}^{\rm NP},\C{10}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-0.64,-0.21)$ & 3.9 \hspace{5mm} \\
  1889. $(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-0.72,0.29)$ & 3.8 \hspace{5mm} \\
  1890. % $(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-0.66,0.03)$ & 2.0 & 23.0
  1891. %$(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-0.69,0.05)$ & 1.9 & 22.0 \hspace{5mm} \\
  1892.  
  1893. \end{tabular}
  1894. \end{column}
  1895. \end{columns}
  1896.  
  1897.  
  1898. \medskip
  1899. \begin{itemize}
  1900. \item $C_9^{NP}$ always play a dominant role
  1901. \item All 2D scenarios above 4$\sigma$ are quite indistinguishable. We have done a systematic study to check
  1902. what are the most relevant Wilson Coefficients to explain all deviations, by allowing progressively different WC to get NP contributions and comparing the pulls.
  1903.  
  1904.  
  1905. \end{itemize}
  1906.  
  1907.  
  1908.  
  1909. \end{minipage}
  1910.  
  1911. \end{footnotesize}
  1912. \vspace*{2.1cm}
  1913. \end{frame}
  1914.  
  1915. %%%%%%%%%%%%%%%%%
  1916.  
  1917. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1918. \begin{frame}{If not NP?}
  1919. {~}
  1920. \begin{minipage}{\textwidth}
  1921. \begin{itemize}
  1922. \item We are not there yet!
  1923. \item There might be something not taken into account in the theory.
  1924. \item Resonances ($\PJpsi$, $\Ppsi(2S)$) tails can mimic NP effects.
  1925. \item There might be some non factorizable QCD corrections.\\
  1926. '' However, the central value of this effect would have to be significantly larger than expected on the basis of existing estimates'' \texttt{D.Straub, 1503.06199}
  1927. .
  1928. \end{itemize}
  1929. \only<1>{
  1930. \begin{center}
  1931.  
  1932. \includegraphics[width=0.9\textwidth]{images/QCDSHIT.png}
  1933. \end{center}
  1934. }
  1935. \only<2>{
  1936. \begin{center}
  1937. \includegraphics[width=0.6\textwidth]{images/charmloop2.png}
  1938. \end{center}
  1939. }
  1940. \only<3>{
  1941. \begin{center}
  1942. \includegraphics[width=0.6\textwidth]{images/charmloop3.png}
  1943. \end{center}
  1944. }
  1945. \end{minipage}
  1946. \vspace*{2.1cm}
  1947. \end{frame}
  1948.  
  1949. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1950. \begin{frame}{If not NP?}
  1951. {~}
  1952. \begin{minipage}{\textwidth}
  1953. \begin{itemize}
  1954. \item How about our clean $P_i$ observables?
  1955. \item The QCD cancel as mentioned only at leading order.
  1956. \item Comparison to normal observables with the optimised ones.
  1957. \end{itemize}
  1958. \includegraphics[width=0.9\textwidth]{images/C9_S_P.png}
  1959.  
  1960.  
  1961. \end{minipage}
  1962. \vspace*{2.1cm}
  1963. \end{frame}
  1964.  
  1965.  
  1966. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1967. % Why flavour physics
  1968. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1969. \begin{frame}
  1970. \begin{center}
  1971. \begin{Huge}
  1972. Disclaimers about some theory predictions
  1973. \end{Huge}
  1974. \end{center}
  1975.  
  1976.  
  1977.  
  1978.  
  1979. \end{frame}
  1980.  
  1981.  
  1982.  
  1983.  
  1984.  
  1985.  
  1986.  
  1987. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  1988. \begin{frame}{Disclaimer}
  1989. {~}
  1990. \begin{footnotesize}
  1991.  
  1992.  
  1993.  
  1994. \begin{minipage}{\textwidth}
  1995. \ARROW \href{http://arxiv.org/abs/1512.07157}{\color{blue}{arXiv:1512.07157}}, Ciuchini, Fedele, Franco, Mishima, Paul, Silvestrini, Valli\\
  1996. \begin{itemize}
  1997. \item Introduce a fully arbitrary parametrization for non-factorizable power correction:
  1998.  
  1999. $$H_\lambda \to H_\lambda + h_\lambda \,\, {\rm where} \,\, h_{\lambda}=h_{\lambda}^{(0)}+h_{\lambda}^{(1)} q^2 + h_{\lambda}^{(2)} q^4 \quad {\rm and} \quad h_{\lambda}^{(0)}\to C_7^{NP}, h_{\lambda}^{(1)}\to C_9^{\rm NP}$$ with ($\lambda=0,\pm$)\hfill(copied from JC'14).\\
  2000. {\bf Complications:} complete lack of theory input/output $\Rightarrow$ {\bf no predictivity} with 18 free parameters (any shape). Specific problems...
  2001.  
  2002. \item The correlator $H_\lambda $ has poles that correspond to the photon the $\PJpsi$. Clearly a 3rd order polynomial cannot approximate this well enough!
  2003.  
  2004.  
  2005.  
  2006. \end{itemize}
  2007. \end{minipage}\end{footnotesize}
  2008. \vspace*{2.1cm}
  2009. \end{frame}
  2010.  
  2011.  
  2012. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  2013. \begin{frame}{More robust calculation of correlator}
  2014. {~}
  2015. \begin{footnotesize}
  2016.  
  2017.  
  2018.  
  2019. \begin{minipage}{\textwidth}
  2020. \begin{center}
  2021. \includegraphics[width=0.5\textwidth]{images/Tom.png}
  2022. \end{center}
  2023. \ARROW Calculate non-local ME at {negative $q^2$} \\[3mm]
  2024. \ARROW Extrapolate to $q^2>0$ via some type of {analytic continuation} \\[3mm]
  2025. \ARROW Use data, when possible, to constrain the extrapolation
  2026.  
  2027. { \footnotesize
  2028.  
  2029. $\qquad \square\ $ We will use $B\to K^* \psi_n$
  2030.  
  2031. $\qquad \square\ $ Cannot use $B\to K^*\mu^+\mu^-$ if $\C9^{\rm NP}$ unknown
  2032.  
  2033. }
  2034.  
  2035. \end{minipage}\end{footnotesize}
  2036. \vspace*{2.1cm}
  2037. \end{frame}
  2038.  
  2039.  
  2040.  
  2041. \begin{frame}{$B\to K^\ast \ell\ell\ $ Amplitudes}
  2042.  
  2043. \small
  2044.  
  2045. \mbox{
  2046. \includegraphics[width=3cm,height=2cm]{bsg0.jpg}\hspace{5mm}
  2047. \includegraphics[width=3cm,height=2cm]{bsg1.jpg}\hspace{5mm}
  2048. \includegraphics[width=3cm,height=2.4cm]{bsg2.jpg}
  2049. }
  2050.  
  2051. \vspace{3mm}
  2052.  
  2053. \mbox{
  2054. \hspace{-10mm}
  2055. \colorbox{llgray}{
  2056. \hspace{1mm}
  2057. $\displaystyle
  2058. A_\lambda^{L,R} = N_\lambda\ \bigg\{
  2059. (C_9 \mp C_{10}) {\blue \F_\lambda(q^2)}
  2060. +\frac{2m_b M_B}{q^2} \bigg[ C_7 {\blue \F_\lambda^{T}(q^2)}
  2061. - 16\pi^2 \frac{M_B}{m_b} {\red \H_\lambda(q^2)} \bigg]
  2062. \bigg\}
  2063. $
  2064. \hspace{2mm}
  2065. }
  2066. }
  2067.  
  2068. \vspace{5mm}
  2069. {\small
  2070.  
  2071. \hspace{-8mm} \btr {\brown Local (Form Factors) :} \hspace{2mm} {\blue $ \F_\lambda^{(T)}(q^2) = \av{\bar M_\lambda(k)| \,\bar s\, \Gamma_\lambda^{(T)}\, b\, | \bar{ B}(k+q)}$}
  2072. \\[5mm]
  2073.  
  2074. \mbox{
  2075. \hspace{-9mm}
  2076. \btr {\brown Non-Local :} \hspace{0mm} {\red $\displaystyle \H_\lambda(q^2) = i \,{\cal P}_\mu^\lambda \int d^4 x\ e^{i q\cdot x}\,
  2077. \av{\bar{M}_\lambda(k)|
  2078. T\big\{ {\cal J}_{\rm em}^\mu(x), \C{i} \, \mathcal{O}(0) \big\} | \bar{B}(q+k)}$}
  2079. }
  2080.  
  2081. \vspace{3mm}
  2082.  
  2083. \hspace{-8mm}
  2084. \btr CKM structure : \hspace{2mm} $\displaystyle \H_\lambda = {\color{gray}- \frac{\lambda_u}{\lambda_t} \H_\lambda^{(u)}} - \frac{\lambda_c}{\lambda_t} \H_\lambda^{(c)}$ \hspace{5mm} $\Rightarrow\ \mathcal{O} \sim (\bar{ c} b)(\bar{ s} c)$
  2085.  
  2086. }
  2087.  
  2088. \end{frame}
  2089.  
  2090.  
  2091.  
  2092.  
  2093.  
  2094. \begin{frame}{Analytic structure of $\H_\lambda(q^2)$}
  2095.  
  2096. \Cite{Bobeth, Chrzaszcz, van Dyk, Virto 1707.07305}
  2097. \vspace{3mm}
  2098.  
  2099.  
  2100. Neglecting OZI- and CKM-suppressed contributions :
  2101.  
  2102. \begin{center}
  2103. \includegraphics[width=7.5cm]{Analyticq2.png}
  2104. \end{center}
  2105.  
  2106.  
  2107. $\displaystyle { \hat{\mathcal{H}}_\lambda(q^2)} = (q^2 - M_{J/\psi}^2)(q^2 -M_{\psi(2S)}^2) \,{ {\mathcal{H}}_\lambda(q^2)} \quad $ has no poles.
  2108.  
  2109. \end{frame}
  2110.  
  2111.  
  2112.  
  2113. \begin{frame}{Accessing $q^2 > 0$ : $\ z\ $ expansion}
  2114.  
  2115. \small
  2116. \Cite{Bobeth, Chrzaszcz, van Dyk, Virto 1707.07305}
  2117. \vspace{2mm}
  2118.  
  2119. \btr Conformal mapping : \hspace{5mm} $q^2 \mapsto \ z\,(q^2) = \frac{\sqrt{t_+ - q^2} - \sqrt{t_+ - t_0}}{\sqrt{t_+ - q^2} + \sqrt{t_+ - t_0}}$
  2120.  
  2121. \mbox{
  2122. \hspace{-10mm}
  2123. \raisebox{8mm}{\includegraphics[width=5.6cm]{Analyticq22.png}}
  2124. \hspace{1mm}
  2125. \includegraphics[width=6.5cm]{Analyticz.png}
  2126. }
  2127.  
  2128. \vspace{-7mm}
  2129.  
  2130. \btr ${\red \hat \H_\lambda (q^2(z))}$ is {\bf analytic in $|z|<1$}\\[3mm]
  2131.  
  2132. \btr Taylor expand $\red \hat{\H}_\lambda(z)$ around $z=0$.\\[3mm]
  2133.  
  2134. \btr Expansion needed for $|z| < 0.52\ $ ( $-7\,\GeV^2 \leq q^2 \leq 14 \GeV^2$ )
  2135.  
  2136.  
  2137. \end{frame}
  2138.  
  2139.  
  2140.  
  2141.  
  2142. \begin{frame}{Accessing $q^2 > 0$ : $\ z\ $ expansion}
  2143. \small
  2144. \Cite{Bobeth, Chrzaszcz, van Dyk, Virto 1707.07305}
  2145.  
  2146. \vspace{3mm}
  2147.  
  2148.  
  2149. \hspace{-5mm} {\bf \brown Some details for actual parametrisation :}
  2150.  
  2151. \mbox{\hspace{-5mm} \btr Try to capture most features of the expansion (better convergence)}
  2152.  
  2153. \mbox{\hspace{-5mm} \btr Parametrize the ratios $\H_\lambda(q^2)/\F_\lambda(q^2)$ instead}
  2154.  
  2155. \mbox{\hspace{-5mm} \btr The poles should not modify the asymptotic behaviour at $|q^2|\to \infty$}
  2156.  
  2157. \begin{eqnarray}
  2158. \H_\lambda(z) &=&
  2159. \frac{1-z\, z^*_{J/\psi}}{z-z_{J/\psi}} \frac{1-z\,z^*_{\psi(2S)}}{z-z_{\psi(2S)}} \ \hat\H_\lambda(z)
  2160. \nonumber\\[2mm]
  2161. %
  2162. \hat\H_\lambda(z) &=& \Big[ \sum_{k=0}^K \alpha_k^{(\lambda)} z^{k} \Big] \F_\lambda(z)
  2163. \nonumber
  2164. \end{eqnarray}
  2165.  
  2166.  
  2167. where $\alpha^{(\lambda)}_k$ are complex coefficients, and the expansion is truncated after the term $z^{K}$.
  2168. We will take $K=2$ ({\brown 16} real parameters).
  2169.  
  2170.  
  2171. \end{frame}
  2172.  
  2173.  
  2174.  
  2175.  
  2176. \begin{frame}{Experimental constraints on $\ z\ $ parametrisation }
  2177. \small
  2178.  
  2179. \vspace{-1mm}
  2180. \hspace{-5mm}
  2181. \Cite{Bobeth, Chrzaszcz, van Dyk, Virto 1707.07305}
  2182. \vspace{1mm}
  2183.  
  2184. \hspace{-5mm} {\bf \brown Experimental constraints :}
  2185.  
  2186. \mbox{\hspace{-5mm} \btr The residues of the poles are given by $B\to K^* \psi_n$ :}
  2187.  
  2188. $$
  2189. \H_\lambda(q^2 \to M_{\psi_n}^2) \sim
  2190. \frac{M_{\psi_n} f^{\,*}_{\psi_n} \A^{\psi_n}_\lambda}{M_B^2 (q^2 - M_{\psi_n}^2)} + \cdots
  2191. $$
  2192.  
  2193. \mbox{\hspace{-5mm} \btr Angular analyses \Cite{Belle, Babar, LHCb} determine : }
  2194.  
  2195. $$
  2196. |r_\perp^{\psi_n}|,\,
  2197. |r_\|^{\psi_n}|,\,
  2198. |r_0^{\psi_n}|,\,
  2199. \arg\{r_\perp^{\psi_n} r_{0}^{\psi_n*}\},\,
  2200. \arg\{r_\|^{\psi_n} r_{0}^{\psi_n*}\},
  2201. $$
  2202.  
  2203. where $\quad \displaystyle r_\lambda^{\psi_n} \equiv \operatorname*{Res}_{q^2\to M^2_{\psi_n}} \frac{\H_\lambda(q^2)}{\F_\lambda(q^2)}
  2204. \sim
  2205. \frac{M_{\psi_n} f^*_{\psi_n} \A^{\psi_n}_\lambda}{M_B^2\, \F_\lambda(M_{\psi_n}^2)}$\\[3mm]
  2206.  
  2207.  
  2208. \mbox{\hspace{-5mm} \btr We produce correlated pseudo-observables from a fit (5+5).}
  2209.  
  2210.  
  2211.  
  2212. \end{frame}
  2213.  
  2214.  
  2215.  
  2216.  
  2217. \begin{frame}{Prior Fit to $\ z\ $ parametrisation }
  2218. \small
  2219.  
  2220. \vspace{-1mm}
  2221. \hspace{-5mm}
  2222. \vspace{1mm}
  2223.  
  2224. \hspace{-5mm} {\bf \brown (Prior) Fit to Experimental and theoretical pseudo-observables :}
  2225.  
  2226.  
  2227.  
  2228. \begin{table}[b]
  2229. % \resizebox{.85\textwidth}{!}{%
  2230. \centering
  2231. \renewcommand{\arraystretch}{1.5}
  2232. \renewcommand{\tabcolsep}{3.1mm}
  2233. \begin{tabular}{@{}crrr@{}}
  2234. \hline
  2235. $k$ & 0\hspace{7mm} & 1\hspace{7mm} & 2\hspace{7mm} \\
  2236. \hline
  2237. %re perp
  2238. ${\rm Re}[\alpha_{k}^{(\perp)}]$ & $-0.06 \pm 0.21$ & $-6.77 \pm 0.27$ & $18.96 \pm 0.59$ \\
  2239. %re para
  2240. ${\rm Re}[\alpha_{k}^{(\parallel)}]$ & $-0.35 \pm 0.62$ & $-3.13 \pm 0.41$ & $12.20 \pm 1.34$ \\
  2241. %re long
  2242. ${\rm Re}[\alpha_{k}^{(0)}]$ & $0.05 \pm 1.52$ & $17.26 \pm 1.64$ & -- \\
  2243. %im perp
  2244. ${\rm Im}[\alpha_{k}^{(\perp)}]$ & $-0.21 \pm 2.25$ & $1.17 \pm 3.58$ & $-0.08 \pm 2.24$ \\
  2245. %im para
  2246. ${\rm Im}[\alpha_{k}^{(\parallel)}]$ & $-0.04 \pm 3.67$ & $-2.14 \pm 2.46$ & $6.03 \pm 2.50$ \\
  2247. %im long
  2248. ${\rm Im}[\alpha_{k}^{(0)}]$ & $-0.05 \pm 4.99$ & $4.29 \pm 3.14$ & -- \\
  2249. \hline
  2250. \end{tabular}
  2251. % }
  2252. \caption{Mean values and standard deviations (in units of $10^{-4}$)
  2253. of the prior PDF for the parameters $\alpha_k^{(\lambda)}$.}
  2254. \label{alphak}
  2255. \end{table}
  2256.  
  2257. \end{frame}
  2258.  
  2259. \begin{frame}{New Physics Analysis }
  2260. \small
  2261.  
  2262. \vspace{-1mm}
  2263. \hspace{-5mm}
  2264. \vspace{1mm}
  2265.  
  2266. \hspace{-5mm} {\bf \brown SM predictions and Fit including $B\to K^* \mu^+\mu^-$ data and $\C{9}^{\rm NP}$ :}\\[4mm]
  2267.  
  2268. \mbox{
  2269. \hspace{-10mm}
  2270. \includegraphics[width=12cm]{NPFit.png}
  2271. }
  2272.  
  2273. The NP hypothesis with {\red $\C{9}^{\bf NP}\sim -1$} is favored strongly in the global fit
  2274.  
  2275. \end{frame}
  2276.  
  2277.  
  2278. \begin{frame}{If NP, what kind?}
  2279.  
  2280. \begin{center}
  2281. \includegraphics[width=0.75\textwidth]{images/criv.png}
  2282. \end{center}
  2283. \ARROW Stolen from A.Crivelin \\
  2284. \ARROW For more comprehensive review see G.Isidori talk:\\
  2285. \href{https://indico.cern.ch/event/646856/contributions/2716924/attachments/1556310/2447567/Implication17b.pdf}{\color{blue}LHCb implications Workshop 2017}
  2286.  
  2287.  
  2288. \end{frame}
  2289.  
  2290. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  2291. \begin{frame}{Conclusions}
  2292. {~}
  2293. \begin{minipage}{\textwidth}
  2294. \begin{itemize}
  2295. \item Clear tensions wrt. SM predictions!
  2296. \item Measurements cluster in the same direction.
  2297. \item We are not opening the champagne yet!
  2298. \item Still need improvement both on theory and experimental side.
  2299. \item Time will tell if this is QCD+fluctuations or new Physics:
  2300. \end{itemize}
  2301. \pause
  2302. ''... when you have eliminated all the\\
  2303. Standard Model explanations, whatever remains,\\
  2304. however improbable, must be New Physics.''\\
  2305.  
  2306. \end{minipage}
  2307. \vspace*{2.1cm}
  2308. \end{frame}
  2309.  
  2310.  
  2311. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  2312. \begin{frame}
  2313. {~}
  2314. \begin{minipage}{\textwidth}
  2315. \begin{center}
  2316. \begin{LARGE}
  2317. Thank you for the attention!
  2318. \end{LARGE}
  2319. \includegraphics[width=0.8\textwidth]{images/Joke.jpg}
  2320.  
  2321. \end{center}
  2322.  
  2323.  
  2324.  
  2325. \end{minipage}
  2326. \vspace*{2.1cm}
  2327. \end{frame}
  2328.  
  2329.  
  2330.  
  2331. \backupbegin
  2332.  
  2333. \begin{frame}\frametitle{Backup}
  2334.  
  2335.  
  2336. \end{frame}
  2337.  
  2338.  
  2339.  
  2340. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  2341. \begin{frame}{Angular analysis of $\PBzero \to \PKstar \Pe \Pe$}
  2342. {~}
  2343. \only<1>{
  2344. \begin{minipage}{\textwidth}
  2345. \begin{itemize}
  2346. \item With the full data set ($3\invfb$) we performed angular analysis in $0.0004 < q^2 <1~\GeV^2$.
  2347. \item Electrons channels are extremely challenging experimentally:
  2348. \begin{itemize}
  2349. \item Bremsstrahlung.
  2350. \item Trigger efficiencies.
  2351. \end{itemize}
  2352. \item Determine the angular observables: $\FL$, $\ATD$, $\ATRe$, $\ATIm$:
  2353. \end{itemize}
  2354. \begin{equation}
  2355. \label{eq:physPars}
  2356. \begin{split}
  2357. \FL &=\frac{|A_0|^2}{|A_0|^2+|A_{||}|^2 + |A_\perp|^2}\\
  2358. \ATD &= \frac{|A_\perp|^2-|A_{||}|^2}{|A_\perp|^2+|A_{||}|^2}\\
  2359. \ATRe &= \frac{2\Real(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2}\\
  2360. \ATIm &= \frac{2\Imag(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2},
  2361. \end{split}\nonumber
  2362. \end{equation}
  2363.  
  2364. \end{minipage}
  2365. }
  2366. \only<2>{
  2367. \begin{center}
  2368. \includegraphics[width=0.5\textwidth]{images/Kstee.png}\\
  2369. \end{center}
  2370. \begin{itemize}
  2371. \item Results in full agreement with the SM.
  2372. \item Similar strength on $C_7$ Wilson coefficient as from $\Pbeauty \to \Pstrange \Pphoton$ decays.
  2373. \end{itemize}
  2374.  
  2375. \begin{center}
  2376. \includegraphics[width=0.9\textwidth]{images/Kstee2.png}
  2377. \end{center}
  2378.  
  2379. }
  2380. \vspace*{2.1cm}
  2381. \end{frame}
  2382.  
  2383. \backupend
  2384.  
  2385. \end{document}