- \documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer}
-
- \usepackage[english]{babel}
- \usepackage{polski}
-
-
- \usetheme[
- bullet=circle, % Other option: square
- bigpagenumber, % circled page number on lower right
- topline=true, % colored bar at the top of the frame
- shadow=false, % Shading for beamer blocks watermark=BG_lower, % png file for the watermark
- ]{Flip}
-
- %\logo{\kern+1.em\includegraphics[height=1cm]{SHiP-3_LightCharcoal}}
-
-
- \usepackage[lf]{berenis}
- \usepackage[LY1]{fontenc}
- \usepackage[utf8]{inputenc}
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- \usefonttheme{professionalfonts}
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- \defaultfontfeatures{Mapping=tex-text} % This seems to be important for mapping glyphs properly
-
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- \setsansfont{Gillius ADF} % This is the font that beamer will use by default
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- \setbeamerfont{title}{family=\fontspec{Gillius ADF}}
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- %\newcommand{\handwriting}{\usefont{T1}{fau}{m}{n}} % From Emerald City, free font
- % \newcommand{\handwriting}{} % If you prefer no special handwriting font or don't have augie
-
- %% Gill Sans doesn't look very nice when boldfaced
- %% This is a hack to use Helvetica instead
- %% Usage: \textbf{\forbold some stuff}
- %\newcommand{\forbold}{\fontspec{Arial}}
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- \usepackage[export]{adjustbox}
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- \usepackage{colortbl}
- \usepackage{mathrsfs} % For Weinberg-esque letters
- \usepackage{cancel} % For "SUSY-breaking" symbol
- \usepackage{slashed} % for slashed characters in math mode
- \usepackage{bbm} % for \mathbbm{1} (unit matrix)
- \usepackage{amsthm} % For theorem environment
- \usepackage{multirow} % For multi row cells in table
- \usepackage{arydshln} % For dashed lines in arrays and tables
- \usepackage{siunitx}
- \usepackage{xhfill}
- \usepackage{grffile}
- \usepackage{textpos}
- \usepackage{subfigure}
- \usepackage{tikz}
-
- %\usepackage{hepparticles}
- \usepackage[italic]{hepparticles}
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- \usepackage{hepnicenames}
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- % Drawing a line
- \tikzstyle{lw} = [line width=20pt]
- \newcommand{\topline}{%
- \tikz[remember picture,overlay] {%
- \draw[crimsonred] ([yshift=-23.5pt]current page.north west)
- -- ([yshift=-23.5pt,xshift=\paperwidth]current page.north west);}}
-
-
-
- % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
- \usepackage{tikzfeynman} % For Feynman diagrams
- \usetikzlibrary{arrows,shapes}
- \usetikzlibrary{trees}
- \usetikzlibrary{matrix,arrows} % For commutative diagram
- % http://www.felixl.de/commu.pdf
- \usetikzlibrary{positioning} % For "above of=" commands
- \usetikzlibrary{calc,through} % For coordinates
- \usetikzlibrary{decorations.pathreplacing} % For curly braces
- % http://www.math.ucla.edu/~getreuer/tikz.html
- \usepackage{pgffor} % For repeating patterns
-
- \usetikzlibrary{decorations.pathmorphing} % For Feynman Diagrams
- \usetikzlibrary{decorations.markings}
- \tikzset{
- % >=stealth', %% Uncomment for more conventional arrows
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- provector/.style={decorate, decoration={snake,amplitude=2.5pt}, draw},
- antivector/.style={decorate, decoration={snake,amplitude=-2.5pt}, draw},
- fermion/.style={draw=gray, postaction={decorate},
- decoration={markings,mark=at position .55 with {\arrow[draw=gray]{>}}}},
- fermionbar/.style={draw=gray, postaction={decorate},
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- decoration={markings,mark=at position .55 with {\arrow[draw=black]{>}}}},
- bigvector/.style={decorate, decoration={snake,amplitude=4pt}, draw},
- }
-
- % TIKZ - for block diagrams,
- % from http://www.texample.net/tikz/examples/control-system-principles/
- % \usetikzlibrary{shapes,arrows}
- \tikzstyle{block} = [draw, rectangle,
- minimum height=3em, minimum width=6em]
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- \graphicspath{{images/}} % Put all images in this directory. Avoids clutter.
-
- % SOME COMMANDS THAT I FIND HANDY
- % \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec
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- \newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold
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- \newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert
- \newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert
- %% "\alert" is already a beamer pre-defined
- \newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}%
-
- \def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}}
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- \makeatletter\let\frametextheight\beamer@frametextheight\makeatother
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- % suppress frame numbering for backup slides
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- }
-
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- \definecolor{links}{HTML}{2A1B81}
- %\hypersetup{colorlinks,linkcolor=,urlcolor=links}
-
- % For shapo's formulas:
- \def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
- \def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
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- %\newcommand{\eqn}[1]{\begin{displaymath} #1 \end{displaymath}}
- \newcommand{\eqa}[1]{\begin{eqnarray} #1 \end{eqnarray}}
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- \newcommand{\apeR}{{A_\perp^R}}
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- \newcommand{\azeL}{{A_0^L}}
- \newcommand{\azeR}{{A_0^R}}
- \newcommand{\azeLR}{{A_0^{L,R}}}
- \newcommand{\Real}{\ensuremath{\mathcal{R}e}\xspace}
- \newcommand{\Imag}{\ensuremath{\mathcal{I}m}\xspace}
-
- \renewcommand{\C}[1]{{\cal C}_{#1}}
- \newcommand{\Ceff}[1]{{\cal C}^{\rm eff}_{#1}}
- \newcommand{\Cpeff}[1]{{\cal C}^{\rm eff\prime}_{#1}}
- \newcommand{\Cp}[1]{{\cal C}^{\prime}_{#1}}
- \def\FL {\ensuremath{F_{\mathrm{L}}}\xspace}
- \def\ATDPH {\ensuremath{A_{\mathrm{T,PR}}^{(2)}}\xspace}
- \def\ATImPH {\ensuremath{A_{\mathrm{T,PR}}^{\mathrm{Im}}}\xspace}
- \def\ATRePH {\ensuremath{A_{\mathrm{T,PR}}^{\mathrm{Re}}}\xspace}
- \def\FLPH {\ensuremath{F_{\mathrm{L,PR}}}\xspace}
- \def\ATDKG {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{(2)}}\xspace}
- \def\ATImKG {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{\mathrm{Im}}}\xspace}
- \def\ATReKG {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{\mathrm{Re}}}\xspace}
- \def\FLKG {\ensuremath{F_{\mathrm{L,\Kstarz \gamma}}}\xspace}
- \def\ATD {\ensuremath{A_{\mathrm{T}}^{(2)}}\xspace}
- \def\ATIm {\ensuremath{A_{\mathrm{T}}^{\mathrm{Im}}}\xspace}
- \def\ATRe {\ensuremath{A_{\mathrm{T}}^{\mathrm{Re}}}\xspace}
- \def\TeV {\ensuremath{\mathrm{TeV}\xspace}}
-
-
- \def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace}
-
-
-
- \newcommand{\disp}{\displaystyle}
- \def\be{\begin{equation}}
- \def\ee{\end{equation}}
- \def\ba{\begin{eqnarray}}
- \def\ea{\end{eqnarray}}
- \def\d{\partial}
- \def\l{\left(}
- \def\r{\right)}
- \def\la{\langle}
- \def\ra{\rangle}
- \def\e{{\rm e}}
- \def\Br{{\rm Br}}
-
- \newcommand{\av}[1]{\langle #1 \rangle}
- % particles
- \def\LstFTTT {\ensuremath{\PLambda^{*}(1520)^{0}}\xspace}
- \def\dll {\ensuremath{\mathrm{DLL}}\xspace}
- \def\Lb {\ensuremath{\PLambda_b}}
-
-
- % useful decays
- \def\BdToKpimm {\decay{\Bd}{\Kp\pim\mumu}}
- \def\BuToKmm {\decay{\Bu}{\Kp\mumu}}
- \def\BsToJPsiKst {\decay{\Bs}{\jpsi\Kstarz}}
- \def\BdTopsitwosKst {\decay{\Bd}{\psitwos\Kstarz}}
- \def\LstFTTTT {\decay{\LstFTTT}{p\Km}}
- %\def\LbToLstmm {\decay{\Lb}{\PLambda^{*}(1520)^{0} \mumu}}
- \def\LbTopKmm {\decay{\Lb}{p\Km\mumu}}
- \def\BuToKmm {\decay{\Bu}{\Kp\mumu}}
- \def\BsTophimm {\decay{\Bs}{\Pphi\mumu}}
-
- % interesting variables
- \def\mkpi {\ensuremath{m_{K\pi}}\xspace}
- \def\mkpimm{\ensuremath{m_{K\pi\mu\mu}}\xspace}
-
- %% peaking background mass hypotheses
- \def\mkmm {\ensuremath{m_{K\mu\mu}}\xspace}
- \def\mSwappKmm {\ensuremath{m_{(\pi\to p)K\mu\mu}}\xspace}
- \def\mSwappiK {\ensuremath{m_{(\pi\to K)K}}\xspace}
- \def\mSwappiKmm {\ensuremath{m_{(\pi\to K)K\mu\mu}}\xspace}
- \def\mSwappK {\ensuremath{m_{(\pi\to p)K}}\xspace}
- \def\mDoubleSwappKmm {\ensuremath{m_{(K\to p)(\pi\to K)\mu\mu}}\xspace}
- \def\mDoubleSwappK {\ensuremath{m_{(K\to p)(\pi\to K)}}\xspace}
- \def\mSwapKst {\ensuremath{m_{K\leftrightarrow\pi}}\xspace}
-
- %% some other decays
- \def\BsToPhimm {\decay{\Bs}{\phi\mumu}}
- \def\BsToPhimmFULL {\decay{\Bs}{\phi(\to\!K^{+}K^{-})\mumu}}
- \def\BsToKKmm {\decay{\Bs}{\Kp\Km\mumu}}
-
- \newcommand{\delC}[1]{\delta {\cal C}_{#1}}
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-
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-
-
-
-
-
- \author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich, IFJ PAN)}
- \institute{UZH}
- \title[Hunting for New Physics phenomena in LHCb experiment]{Hunting for New Physics phenomena in LHCb experiment}
- \date{25 September 2014}
-
-
- \begin{document}
- \tikzstyle{every picture}+=[remember picture]
- {
- \setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
- \begin{frame}[c]%{\phantom{title page}}
- \begin{center}
- \begin{center}
- \begin{columns}
- \begin{column}{0.9\textwidth}
- \flushright\fontspec{Trebuchet MS}\bfseries \Huge {Hunting for New Physics phenomena in LHCb experiment}
- \end{column}
- \begin{column}{0.2\textwidth}
- %\includegraphics[width=\textwidth]{SHiP-2}
- \end{column}
- \end{columns}
- \end{center}
- \quad
- \vspace{3em}
- \begin{columns}
- \begin{column}{0.44\textwidth}
- \flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
-
- \end{column}
- \begin{column}{0.53\textwidth}
- \includegraphics[height=1.3cm]{uzh-transp}{~}{~}
- \includegraphics[height=1.1cm]{ifj.png}
- \end{column}
- \end{columns}
-
- \vspace{1em}
- % \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
- \vspace{0.5em}
- \textcolor{normal text.fg!50!Comment}{IFJ PAN \\November 24, 2016}
- \end{center}
- \end{frame}
- }
-
-
- \begin{frame}{Outline}
-
- \begin{minipage}{\textwidth}
- {~}\\
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %% tau ->3mu
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-
-
-
-
-
-
- \begin{enumerate}
- \item Why flavour is important.
- \item LHCb detector.
- \item Lepton Flavour Violation.
- \item Dark Boson searches.
- \item Electroweak penguins.
- \item Measurement of Higher $\PKstar$ states in Electroweak Penguin decays.
- \item Theory interpretation.
- \item Disclaimers about some theory predictions.
- \item Conclusions.
- \end{enumerate}
-
-
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % Why flavour physics
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- \begin{center}
- \begin{Huge}
- Why Flavour is important?
- \end{Huge}
- \end{center}
-
-
-
-
- \end{frame}
-
-
-
- \begin{frame}{A lesson from history - GIM mechanism}
- \begin{minipage}{\textwidth}
-
- \begin{center}
- \includegraphics[width=0.62\textwidth]{images/GIM2.png}
- \end{center}
- \begin{columns}
- \column{0.7\textwidth}
- \begin{itemize}
- \begin{footnotesize}
-
-
- \item Cabibbo angle was successful in explaining dozens of decay rates in the 1960s.
- \item There was, however, one that was not observed by experiments: $\PKzero \to \Pmuon \APmuon$.
- \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.
- \item At that point most of the people were skeptical about that. Fortunately in 1974 the discovery of the $\PJpsi$ meson silenced the skeptics.
- \end{footnotesize}
- \end{itemize}
- \column{0.3\textwidth}
- \begin{center}
- \includegraphics[width=0.95\textwidth]{images/GIM3.png}\\
- \includegraphics[width=0.7\textwidth]{images/604.jpg}\\{~}\\{~}
- \end{center}
- \end{columns}
-
-
-
- \end{minipage}
-
- \vspace*{2.1cm}
- \end{frame}
-
- \begin{frame}{A lesson from history - CKM matrix}
- \begin{minipage}{\textwidth}
-
- \begin{center}
- {~}\\{~}\\
- \includegraphics[width=0.5\textwidth]{images/CKMmatrix.png}
-
- \end{center}
- \begin{columns}
- \column{0.6\textwidth}
- \begin{itemize}
- \begin{small}
-
-
-
-
- \item Similarly, CP violation was discovered in 1960s in the neutral kaons decays.
- \item $2 \times 2$ Cabbibo matrix could not allow for any CP violation.
- \item For CP violation to be possible one needs at least a $3 \times 3$ unitary matrix \\ $\looparrowright$ Cabibbo-Kobayashi-Maskawa matrix (1973).
- \item It predicts existence of $\Pbottom$ (1977) and $\Ptop$ (1995) quarks.
- \end{small}
-
- \end{itemize}
- \column{0.4\textwidth}
- \begin{center}
- {~}
- %\includegraphics[height=2cm]{images/CP.png}\\
- \includegraphics[width=0.96\textwidth]{bottom.jpg}
-
- \end{center}
- \end{columns}
-
-
-
- \end{minipage}
-
- \vspace*{2.1cm}
- \end{frame}
-
-
- \begin{frame}{A lesson from history - Weak neutral current}
- \begin{minipage}{\textwidth}
-
- \begin{center}
- \includegraphics[height=3cm]{images/weakcurr.png}{~}
- \includegraphics[height=3cm]{images/weakcurr2.png}
- \end{center}
-
- \begin{columns}
- \column{0.6\textwidth}
- \begin{itemize}
- \begin{small}
-
-
- \item Weak neutral currents were first introduced in 1958 by Buldman.
- \item Later on they were naturally incorporated into unification of weak and electromagnetic interactions.
- \item 't Hooft proved that the GWS models was renormalizable.
- \item Everything was there on theory side, only missing piece was the experiment, till 1973.
- \end{small}
-
- \end{itemize}
- \column{0.4\textwidth}
- \begin{center}
- {~}
- %\includegraphics[height=2cm]{images/CP.png}\\
- \includegraphics[width=0.85\textwidth]{images/bubblecern.png}
- \end{center}
- \end{columns}
-
-
-
- \end{minipage}
-
- \vspace*{2.1cm}
- \end{frame}
-
- \begin{frame}
- \begin{center}
- \begin{Huge}
- LHCb detector
- \end{Huge}
- \end{center}
-
-
-
-
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % DETECTOR
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- \only<1>{\frametitle{LHCb detector - tracking}
- \begin{columns}
- \column{3in}
- \includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
-
- \column{2in}
- \includegraphics[width=0.95\textwidth]{images/sketch.png}
- \end{columns}
- \begin{itemize}
- \item Excellent Impact Parameter (IP) resolution ($20~\rm \mu m$).\\
- $\Rightarrow$ Identify secondary vertices from heavy flavour decays
- \item Proper time resolution $\sim~40~\rm fs$.\\
- $\Rightarrow$ Good separation of primary and secondary vertices.
- \item Excellent momentum ($\delta p/p \sim 0.4 - 0.6\%$) and inv. mass resolution.\\
- $\Rightarrow$ Low combinatorial background.
-
- \end{itemize}
-
-
- }
-
- \only<2>{\frametitle{LHCb detector - particle identification}
- \begin{columns}
- \column{3in}
- \includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
-
- \column{2in}
- \includegraphics[width=0.95\textwidth]{images/cher.png}
- \end{columns}
- \begin{itemize}
- \item Excellent Muon identification $\epsilon_{\mu \to \mu} \sim 97\%$, $\epsilon_{\pi \to \mu} \sim 1-3\%$
- \item Good $\PK-\Ppi$ separation via RICH detectors, $\epsilon_{\PK \to \PK} \sim 95\%$, $\epsilon_{\Ppi \to \PK} \sim 5\%$.\\
- $\Rightarrow$ Reject peaking backgrounds.
- \item High trigger efficiencies, low momentum thresholds.
- Muons: $p_T > 1.76 \GeV$ at L0, $p_T > 1.0 \GeV$ at HLT1,\\
- $B \to \PJpsi X $: Trigger $\sim 90\%$.
-
- \end{itemize}
-
-
- }
-
-
- \end{frame}
-
-
-
- \begin{frame}
-
- \begin{center}
- \begin{Huge}
- Lepton Flavour Violation
- \end{Huge}
- \end{center}
-
-
-
- \end{frame}
-
-
-
-
- \begin{frame}\frametitle{Lepton Flavour/Number Violation}
-
-
- \begin{enumerate}
- \item Lepton Flavour Violation (LFV) found in neutrino sector - the first phenomena outside the Standard Model.
- \item The search for charged lepton flavour violation (CLFV) commenced with muon discovery (1936) and its identification as a separate particle.
- \end{enumerate}
- \begin{columns}
- \column{3in}
- \begin{itemize}
- \item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$
- \item Unless there is another $\Pnu$.
- \end{itemize}
-
- \column{2in}
- {~}\includegraphics[width=0.98\textwidth]{images/rabi.png}
-
- \end{columns}
- \begin{footnotesize}
-
- \begin{enumerate}
- \setcounter{enumi}{2}
- \item The observation of CLFV would be a clear signature of New Physics (NP) - paramount importance for flavour physics and the enigma of generations.
- \item LFV vs LNV (Lepton Number Violation)
- \end{enumerate}\end{footnotesize}
- \begin{columns}
- \column{3.5in}
- \begin{footnotesize}
-
-
- \begin{itemize}
- \item Even with LFV, lepton number can be a conserved quantity.
- \item Many NP models predict LNV (Majorana neutrinos)
- \item LNV searched in so-called neutrinoless double $\beta$ decays.
- \end{itemize}
- \end{footnotesize}
- \column{1.5in}
- \includegraphics[width=0.65\textwidth]{images/Double_beta_decay_feynman.png}
-
- \end{columns}
-
-
- % \textref{M.Chrz\k{a}szcz 2014}
-
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- \frametitle{Status of searches for $ \tau \to \mu \mu \mu$}
- \begin{columns}
- \begin{column}{.55\textwidth}
-
- \includegraphics[width=.90\textwidth]{feymn.png}
-
- {{
- \begin{small}
- \begin{itemize}
- \item Charged Lepton Flavour Violation process.
- \item The Standard Model contribution: penguin diagram with neutrino oscillation.
- \item Negligible SM branching fraction.
- \item Large enhacement from NP models like: SUSY, Little Higgs, Fourth generation, etc.
-
- % \item SM prediction is beyond experimental reach~$O(10^{-40})$.
-
- \end{itemize}
- \end{small}
- }}
- \end{column}
- \begin{column}{.45\textwidth}
-
- \begin{alertblock}{Predictions}
- \begin{description}
- \item[SM] $ O(10^{-40})$
- \item[var.\ SUSY] $10^{-10}$
- \item[non universal $\color{green}{Z'}$] $10^{-8}$
- \item[mSUGRA+seesaw] $10^{-9}$
- \item[and many more...]
- \end{description}
- \end{alertblock}
-
- \begin{alertblock}{Current limits ($ \color{white} 90\,\%$ CL)}
-
- \begin{description}
- \item[BaBar] $3.3\times 10^{-8}$
- \item[Belle] $2.1\times 10^{-8}$
- \end{description}
- \end{alertblock}
- \includegraphics[width=.63\textwidth]{SUSY.png}
-
- \end{column}
-
- \end{columns}
-
-
- \end{frame}
-
- \iffalse
-
- \begin{frame} \frametitle{Strategy}
- \begin{enumerate}
- \item Data sample: $1 \invfb~7~\TeV$ and $2 \invfb~8\TeV$.
- \item Normalization (control) decay channel: $\PDs\to\Pphi(\Pmu\Pmu)\Ppi$.
- \item Blind analysis in the region of $| m_{\mu\mu\mu} - m_{\tau} | <20~\MeV/c^2$.
- \item Event selection:
- \begin{itemize}
- \item Preselection of three tracks that combine to give a mass close to $m_{\tau}$, with displaced vertex.
- \item Selection based on three classifiers:
- \begin{itemize}
- \item Geometry and topology ($\mathcal{M}_{3body}$) - multivariate classifier
- \item PID ($\mathcal{M}_{PID}$) - multivariate classifier
- \item Three muon invariant mass ($m_{\mu\mu\mu}$)
- \end{itemize}
- \end{itemize}
- \item Major background contributions:$\PDs \to \eta(\mu\mu\gamma) \mu \nu$ and $\PD \to \PK \Ppi \Ppi$ decays.
- \item Evaluation of the upper limit on $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)$ using $\rm CL_s$ method.
- \end{enumerate}
-
-
- \end{frame}
- \fi
-
-
- \begin{frame}
- \frametitle{$\tau$ production at LHCb}
- \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{Multivariate Analysis}
- \begin{minipage}{\textwidth}
-
- \begin{columns}
- \column{0.1in}
- {~}\\
- \column{2.9in}
- \ARROW First usage of of the blending \\technique in HEP!\\
- \ARROW Each $\tau$ source has it's own ''targer'' classifier.\\
- \ARROW 5 classifiers are then ''blended'' together.\\
- \ARROW Gain $6\%$ on signal efficiency.\\
- \begin{exampleblock}{}
- Up to today the most advanced MVA used in LHCb!
- \end{exampleblock}
- ~\\
- \ARROW Calibrated on data using $\PDs \to \phi \pi$
- \includegraphics[angle=-90,width=.6\textwidth]{m3body_2012.pdf}
-
- \column{2in}
- \includegraphics[width=.99\textwidth]{images/diagram.png}\\
- \includegraphics[angle=-90, width=.98\textwidth]{images/mixing.pdf}
-
- \end{columns}
-
-
- \end{minipage}
- \end{frame}
-
- \iffalse
- \begin{frame}
- \frametitle{Optimization}
- \begin{minipage}{\textwidth}
-
- \begin{footnotesize}
- \begin{itemize}
- \item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane.
- \item In 2D we collect the events in groups(bins)
- \item Bins are optimised using $CL_s$ method:
- \begin{equation}
- CL_s = \dfrac{\prod_{i=1}^{N_{\text{chan}}}\sum_{n=0}^{n_i} \dfrac{e^{-(s_i+b_i)} (s_i+b_i)^{n}}{n!} }{\prod_{i=1}^{n_{\text{chan}}} \sum_{n=0}^{n_i} \dfrac{e^{-b_i} b_i^{n}}{n!}} \nonumber~,
- \end{equation}
- \end{itemize}
- \end{footnotesize}
- \begin{center}
- \includegraphics[width=.6\textwidth]{images/rank.pdf}
-
- \end{center}
-
-
-
- \end{minipage}
- \end{frame}
- \fi
- \iffalse
- \begin{frame}
- \frametitle{Relative normalisation}
- $\boxed{\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}}$
- \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 data.
- \end{itemize}
- \begin{columns}
- \column{2.3in}
- \center{2011}\\
-
- \includegraphics[angle=-90,width=.97\textwidth]{images/Ds_data_2011.pdf}
- \column{2.3in}
- \center{2012}\\
- \includegraphics[angle=-90,width=.97\textwidth]{images/Ds_data_2012.pdf}
- \end{columns}
- \end{frame}
-
-
- \fi
-
-
-
-
-
- \begin{frame}
- \frametitle{Model dependence}
- \begin{itemize}
- \begin{small}
- \item Model description in \href{http://arxiv.org/abs/0707.0988}{\color{blue}\texttt{arXiv:0707.0988}} by S.Turczyk using Effective Field Theory approach.
- \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms.
- \item All five cases implemented in TAUOLA.
- \end{small}
- \end{itemize}
-
-
- \only<1>{
- \begin{columns}
- \column{0.33\textwidth}
- \includegraphics[angle=-90,width=.78\textwidth]{images/LLLL.pdf}\\
- \includegraphics[angle=-90,width=.78\textwidth]{images/LLRR.pdf}\\
-
-
- \column{0.33\textwidth}
- \includegraphics[angle=-90,width=.78\textwidth]{images/LLLLRAD.pdf}\\
- \includegraphics[angle=-90,width=.78\textwidth]{images/LLRRRAD.pdf}
-
- \column{0.33\textwidth}
- \includegraphics[angle=-90,width=.78\textwidth]{images/RAD.pdf}\\
- \begin{small}
-
- \begin{exampleblock}{}
- M.Chrzaszcz, T.Przedzinski, Z.Was, J.Zareba\\ \href{https://arxiv.org/abs/1609.04617}{\color{blue}\texttt{arXiv:1609.04617 }}\\{~}\\
-
- \end{exampleblock}
- {~}\\
- \end{small}
-
-
- % \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{Results}
-
- \begin{center}
- \includegraphics[angle=-90,width=0.65\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{Combination of LFV UL}
-
- \ARROW To ''squeeze'' the most of the LFV New Physics exclusions there was an idea to combine the limits for LHCb and B factories.\\
- \ARROW As a result I have been enrolled as HFAG member.\\
- \begin{exampleblock}{}
- $\tau \to \mu \mu \mu$ is the most cited number of the HFAG report!!!\\
- \end{exampleblock}
- {~}\\
- \includegraphics[width=0.9\textwidth]{images/TauLFV_UL_2014001_averaged.png}
-
- \begin{exampleblock}{}
- \texttt{arXiv:1412.7515}, [HFAG, M.Chrzaszcz, et. al.]
- \end{exampleblock}
-
- \end{frame}
-
-
-
- \begin{frame}
-
- \begin{center}
- \begin{Huge}
- Dark Boson searches
- \end{Huge}
- \end{center}
-
-
-
- \end{frame}
-
-
- \begin{frame}\frametitle{Generalize Higgs potential}
-
- \begin{minipage}{\textwidth}
- \begin{small}
-
-
- \ARROW The model is extremely simple:
- \begin{align*}
- V(H,S)=V_H + V_{\rm mix} + V_S,
- \end{align*}
- where
- \begin{columns}
- \column{0.1in}
- {~}\\
- \column{2.9in}
- \begin{align*}
- V_H = -\mu^2 H^{\dag}H + \lambda_H (H^{\dag} H)^2\\
- V_{\rm mix} = \frac{a_1}{2}\left(H^{\dag}H\right)S + \frac{a_2}{2}\left(H^{\dag}H\right)S^2\\
- V_S = \frac{b_2}{2}S^2 + \frac{b_3}{3}S^3 + \frac{b_4}{4}S^4
- \end{align*}
- \column{2in}
- \begin{center}
- \includegraphics[width=0.95\textwidth]{images/h.png}
- \end{center}
- \end{columns}
-
- \ARROW The main advantage of this potential is that it fixes the inflation problem.\\
- \ARROW Now the Lagrangian needs to be written in physical degrees of freedom\\
- \ARROW Then you generate the mass is given(see backup for details):
-
- \begin{align*}
- \begin{pmatrix}
- h \\
- s
- \end{pmatrix}=
- \begin{pmatrix}
- \sin \theta & \cos \theta \\
- \cos \theta & \sin \theta
- \end{pmatrix}
- \begin{pmatrix}
- s^{\prime}\\
- h^{\prime}
- \end{pmatrix}
- \end{align*}
-
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
-
-
- \end{frame}
-
- \begin{frame}\frametitle{Implications for Flavour}
- \begin{minipage}{\textwidth}
- \begin{small}
- {~}\\
- \ARROW The mixing angle between the Higgs and the Inflaton has to be small.\\
- \ARROW Typically if $m_H=125~\GeV$ then $m_S \sim \mathcal{O}(1)~\GeV$.\\
- \ARROW If yes we can look for this in $\PB$ decays:
- \begin{columns}
- \column{0.1in}
- {~}\\
- \column{3.4in}
- \begin{equation}
- {\rm Br} (\PB \to \chi X_s) ~\sim 10^{-6}\left(1-\frac{m^2_{\chi}}{m^2_b}\right) \left(\frac{\beta}{\beta_0}\right) \left(\frac{300{\rm MeV}}{m_{\chi}}\right)\nonumber
- \end{equation}
-
- \column{1.5in}
- \begin{center}
- \includegraphics[width=0.95\textwidth]{images/diagram.pdf}
- \end{center}
-
- \end{columns}
- \ARROW The inflaton has a small width and non zero life-time. \\
- \ARROW The analysis is a peak search.\\
- \begin{exampleblock}{}
- It has passed the collaboration review and will be shown first time by my PhD student at the Epiphany conference.
- \end{exampleblock}
-
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
- \begin{frame}\frametitle{RIP Inflaton}
- \begin{minipage}{\textwidth}
- \begin{small}
-
-
-
- \begin{center}
- \includegraphics[angle=-90,width=0.9\textwidth]{{images/Inflaton_parameter_space_log}.pdf}
- \end{center}
-
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
- \iffalse
- \begin{frame}[c]{The inflaton model, so what?}
- \begin{minipage}{\textwidth}
- \begin{small}
- {~}\\
- \ARROW Now if we look how many of the $X_s$ are $\PK$ and $\PKstar$ we define the variables:
- \begin{align*}
- r_K = \frac{\PB \to \PK \chi}{\PB \to X_s \chi}~~~~r_{\PKstar} = \frac{\PB \to \PKstar \chi}{\PB \to X_s \chi}
- \end{align*}
- \includegraphics[width=0.45\linewidth]{images/rk_graph.png}
- \includegraphics[width=0.45\linewidth]{images/rkstar.png} \\
- {~}\\
- \ARROW So the assumption about $33~\%$ was generous assumption.
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
- \fi
-
-
- \begin{frame}
-
- \begin{center}
- \begin{Huge}
- Electroweak penguins
- \end{Huge}
- \end{center}
-
-
-
- \end{frame}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}\frametitle{Why Electroweak penguins?}
-
- \begin{columns}
- \column{4in}
- \begin{itemize}
- \item The SM allows only the charged interactions to change flavour.
- \begin{itemize}
- \item Other interactions are flavour conserving.
- \end{itemize}
- \item One can escape this constraint and produce $\Pbottom \to \Pstrange$ and $\Pbottom \to \Pdown$ at loop level.
- \begin{itemize}
- \item These kind of processes are suppressed in SM $\to$~Rare decays.
- \item New Physics can enter in the loops.
- \end{itemize}
- \end{itemize}
- \begin{center}
- \includegraphics[scale=0.3]{lupa.png}
- \includegraphics[scale=0.3]{example.png}
- \end{center}
- \column{1.5in}
- \includegraphics[width=0.61\textwidth]{couplings.png}
- \end{columns}
-
- \end{frame}
-
-
- \begin{frame}{Tools in rare $\PBzero$ decays}
- {~}
- \begin{minipage}{\textwidth}
-
- \begin{itemize}
- \item \textbf{Operator Product Expansion and Effective Field Theory}
- \end{itemize}
- \begin{columns}
- \column{0.1in}{~}
- \column{3.2in}
- \begin{footnotesize}
-
-
- \begin{align*}
- H_{eff} = - \dfrac{4G_f}{\sqrt{2}} V V^{\prime \ast}\ \sum_i \left[\underbrace{C_i(\mu)O_i(\mu)}_\text{left-handed} +\
- \underbrace{C'_i(\mu)O'_i(\mu)}_\text{right-handed}\right],
- \end{align*}
- \end{footnotesize}
- \column{2in}
- \begin{tiny}
- \begin{description}
- \item[i=1,2] Tree
- \item[i=3-6,8] Gluon penguin
- \item[i=7] Photon penguin
- \item[i=9.10] EW penguin
- \item[i=S] Scalar penguin
- \item[i=P] Pseudoscalar penguin
- \end{description}
-
- \end{tiny}
- \end{columns}
- where $C_i$ are the Wilson coefficients and $O_i$ are the corresponding effective operators.
- \begin{center}
- \includegraphics[width=0.85\textwidth,height=3cm]{images/all.png}
-
- \end{center}
-
-
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- \iffalse
-
- \begin{frame}{Analysis of Rare decays}
- \begin{footnotesize}
-
- %{\Large Since a long time ago...} \\ \medskip
- %\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. \\
- %\medskip
- %\medskip
- %\hfill....... with not much success till 2013.\hspace*{1cm}
- %\bigskip
-
- Analysis of FCNC in a model-independent approach, effective Hamiltonian:
- \vspace*{-0.1cm}
- \begin{columns}
- \begin{column}{1cm}
- ~
- \end{column}
- \begin{column}{8cm}
- \begin{equation*}
- b\to s\gamma(^*): {\mathcal H}^{SM}_{\Delta F=1} \propto
- \sum_{i=1}^{10} V_{ts}^* V_{tb} {\cgreen \C{i}} \alert{ {\cal O}_i} + \ldots
- \end{equation*}
-
- \vspace{-0.2cm}
-
- \begin{itemize}
- \item $\alert{ {\cal O}_7} = \frac{e}{16 \pi^2}m_b\,
- (\bar s\sigma^{\mu\nu} P_R b) F_{\mu\nu}\,$ %\quad [real or soft photon]
- \item $\alert{ {\cal O}_9}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b)\ (\bar\ell\gamma_\mu\ell)$
- %\quad [$b\to s\mu\mu$ via $Z$/hard $\gamma$]
- \item $\alert{ {\cal O}_{10}}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b) \ (\bar\ell\gamma_\mu\gamma_5\ell)$, ...
- %\quad [$b\to s\mu\mu$ via $Z$]
- \end{itemize}
- \end{column}
- \begin{column}{5.5cm}
- \includegraphics[width=3.5cm]{images/qum1.png}
- %\includegraphics[width=3cm]{bsll.pdf}
- \end{column}
- \end{columns}
-
- %\hspace*{5cm} with no clear success yet...
- %\bigskip
-
-
- %\centerline{{\bf Goal}: \underline{Decode the short distance physics to find a smoking gun of BSM}\hspace*{2cm}}
-
-
- \bigskip
- \hspace*{0.0cm} $\bullet$ {\bf SM} Wilson coefficients up to NNLO + e.m. corrections at $\mu_{ref}=4.8$ GeV [{\cgreen Misiak et al.}]: $${\cal C}_7^{\rm SM}=-0.29,\, {\cal C}_9^{\rm SM}=4.1,\, {\cal C}_{10}^{\rm SM}=-4.3$$
- %BUT, like in the film there is always the good, the bad and the ugly.
- \bigskip
- $\bullet$ {\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
-
-
- \end{footnotesize}
-
- \end{frame}
-
- \fi
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
- \iffalse
- %%%%%%%%%%%%%%%%%%%%5
- \begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$, where it all begun}
- {~}
- \begin{minipage}{\textwidth}
- \only<1>{
- \begin{columns}
- \column{0.6\textwidth}
- August 2013:\\
-
- \includegraphics[width=0.95\textwidth]{images/P5prime.png}
- \column{0.4\textwidth}
- \begin{itemize}
- \item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
- \item It turned out that the discrepancy occurred in an observable that was not constrained.
- \item $q^2$ is the dimuon invariant mass.
-
- \end{itemize}
- \end{columns}
-
-
- }
-
-
-
-
- \only<2>{
-
-
- \begin{columns}
- \column{0.6\textwidth}
- August 2013:\\
-
- \includegraphics[width=0.95\textwidth]{images/P5prime.png}
- \column{0.4\textwidth}
- \begin{itemize}
- \item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
- \item It turned out that the discrepancy occurred in an observable that was not constrained.
-
- \end{itemize}
- \end{columns}
-
-
- \begin{exampleblock}{}
- Now let's move back and see the theory behind the $\PBzero \to \PKstar \Pmuon \APmuon$ and $P_5^{\prime}$.
- \end{exampleblock}
- }
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \fi
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$ kinematics}
- {~}
- \begin{minipage}{\textwidth}
-
- $\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.
-
-
- \only<1>{
- {\tiny{
- \eqa{\label{dist}
- \frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi}&=&\frac9{32\pi} \bigg[
- \frac{3}{4} (1- F_L) \sin^2\theta_K + F_L \cos^2\theta_K \nn\\[1.5mm] &&\hspace{-2.7cm} + \left(\frac{1}{4}(1-F_L) \sin^2\theta_K - F_L \cos^2\theta_K\right) \cos 2\theta_l\nn\\[1.5mm]
- &&\hspace{-2.7cm}+ S_3 \sin^2\theta_K \sin^2\theta_l \cos 2\phi + S_4 \sin 2\theta_K \sin 2\theta_l \cos\phi + S_5 \sin 2\theta_K \sin\theta_l \cos\phi \nn\\[1.5mm]
- &&\hspace{-2.7cm}+ (S_{6s} \sin^2\theta_K + {S_{6c} \cos^2\theta_K}) \cos\theta_l
- + S_7 \sin 2\theta_K \sin\theta_l \sin\phi + S_8 \sin 2\theta_K \sin 2\theta_l \sin\phi \nn\\[1.5mm]
- &&\hspace{-2.7cm}+ S_9 \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,,
- \nonumber}
- }}
- $\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decay.
-
- }
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
- \iffalse
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Transversity amplitudes }
- {~}
- \begin{minipage}{\textwidth}
-
- $\color{JungleGreen}{\Rrightarrow}$ One can link the angular observables to transversity amplitudes
- {\tiny{
- \eqa{
- J_{1s} & = & \frac{(2+\beta_\ell^2)}{4} \left[|\apeL|^2 + |\apaL|^2 +|\apeR|^2 + |\apaR|^2 \right]
- + \frac{4 m_\ell^2}{q^2} \re\left(\apeL\apeR^* + \apaL\apaR^*\right)\,,\nn\\[1mm]
- %
- 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]
- %
- J_{2s} & = & \frac{ \beta_\ell^2}{4}\left[ |\apeL|^2+ |\apaL|^2 + |\apeR|^2+ |\apaR|^2\right],
- \hspace{0.92cm} J_{2c} = - \beta_\ell^2\left[|\azeL|^2 + |\azeR|^2 \right]\,,\nn\\[1mm]
- %
- J_3 & = & \frac{1}{2}\beta_\ell^2\left[ |\apeL|^2 - |\apaL|^2 + |\apeR|^2 - |\apaR|^2\right],
- \qquad J_4 = \frac{1}{\sqrt{2}}\beta_\ell^2\left[\re (\azeL\apaL^* + \azeR\apaR^* )\right],\nn \\[1mm]
- %
- J_5 & = & \sqrt{2}\beta_\ell\,\Big[\re(\azeL\apeL^* - \azeR\apeR^* ) - \frac{m_\ell}{\sqrt{q^2}}\,
- \re(\apaL A_S^*+ \apaR^* A_S) \Big]\,,\nn\\[1mm]
- %
- J_{6s} & = & 2\beta_\ell\left[\re (\apaL\apeL^* - \apaR\apeR^*) \right]\,,
- \hspace{2.25cm} J_{6c} = 4\beta_\ell\, \frac{m_\ell}{\sqrt{q^2}}\, \re (\azeL A_S^*+ \azeR^* A_S)\,,\nn\\[1mm]
- %
- J_7 & = & \sqrt{2} \beta_\ell\, \Big[\im (\azeL\apaL^* - \azeR\apaR^* ) +
- \frac{m_\ell}{\sqrt{q^2}}\, \im (\apeL A_S^* - \apeR^* A_S)) \Big]\,,\nn\\[1mm]
- %
- J_8 & = & \frac{1}{\sqrt{2}}\beta_\ell^2\left[\im(\azeL\apeL^* + \azeR\apeR^*)\right]\,,
- %
- \hspace{1.9cm} J_9 = \beta_\ell^2\left[\im (\apaL^{*}\apeL + \apaR^{*}\apeR)\right] \,,
- \label{Js}\nonumber}
- }}
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Link to effective operators}
- {~}
- \begin{minipage}{\textwidth}
- $\color{JungleGreen}{\Rrightarrow}$ So here is where the magic happens. At leading order the amplitudes can be written as:
- {\tiny{
- \eqa{
- \apeLR &=&\sqrt{2} N m_B(1- \hat s)\bigg[ (\Ceff9 + \Cpeff9) \mp (\C{10} + \Cp{10})
- +\frac{2\hat{m}_b}{\hat s} (\Ceff7 + \Cpeff7) \bigg]\xi_{\bot}(E_{K^*}) \nn \\[2mm]
- \apaLR &=& -\sqrt{2} N m_B (1-\hat s)\bigg[(\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10})
- +\frac{2\hat{m}_b}{\hat s}(\Ceff7 - \Cpeff7) \bigg] \xi_{\bot}(E_{K^*}) \nn \\[2mm]
- \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^*}),
- \label{LargeRecoilAs}\nonumber}
- }}
- where $\hat s = q^2 /m_B^2$, $\hat{m}_i = m_i/m_B$. The $\xi_{\|,\bot }$ are the form factors. \\
-
- \only<1>{
- \ARROW In practice one measures normalized $J$ by branching fractions:
- \begin{equation*}
- S_i/A_i = \frac{J_i \pm \overline{J}_i}{d\Gamma + d \overline{\Gamma}/dq^2}
- \end{equation*}
-
-
- }
- \only<2>{
- $\color{JungleGreen}{\Rrightarrow}$ Now we can construct observables that cancel the $\xi$ form factors at leading order:
- \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
- }
- }
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- \begin{center}
- \begin{Huge}
- LHCb measurement of $\PBd \to \PKstar \Pmu \Pmu$
- \end{Huge}
- \end{center}
-
-
-
-
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{LHCbs $\PBzero \to \PKstar \Pmuon \APmuon$, Selection}
- {~}
- \begin{minipage}{\textwidth}
- \begin{footnotesize}
- \begin{columns}
- \column{0.2in}
- {~}
- \column{2in}
- \ARROW Trigger
- \begin{itemize}
- \item Muon trigger.
- \item Topological trigger.
- \end{itemize}
- \ARROW Good modelling with MC. \\
- \ARROW Selection:
- \begin{itemize}
- \item As loose as possible.
- \item Based on the $\PBzero$ vertex quality, impact parameters, loose Particle identification for the hadrons.
- \item The variables were chosen in a way we are sure the are correctly modelled in MC.
- \end{itemize}
- \column{2.8in}
-
- \includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_pt}.pdf}\\
- \includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_costhetal}.pdf}
- \end{columns}
-
-
-
- \end{footnotesize}
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
- \fi
- \iffalse
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Peaking backgrounds}
- {~}
- \begin{minipage}{\textwidth}
- \begin{footnotesize}
- \ARROW A number of peaking backgrounds that can mistaken as your signal.\\
- \ARROW There where a specially designed vetoes to fight each of them.
- \begin{center}
- \begin{tiny}
- \hspace{-1cm}\begin{tabular}{ r | c c | c c }
- \hline
- & \multicolumn{2}{c|}{after preselection, before vetoes} & \multicolumn{2}{c }{after vetoes and selection}\\
- Channel & Estimated events & \% signal & Estimated events & \% signal \\
- \hline
- \hline
- $\PLambda_b \to \PLambda^{\ast}(1520)^{0} \mu\mu$ &$ (1.0\pm0.5)\times10^3 $&$ 19\pm8 $&$ 51\pm25 $&$ 1.0\pm0.4$\\
- $\PLambda_b \to {\rm p } \PK \mu\mu$ &$ (1.0\pm0.5)\times10^2 $&$ 1.9\pm0.8 $&$ 5.7\pm2.8 $&$ 0.11\pm0.05$ \\
- $\PBd \to \PKplus \mu \mu$ &$ 28\pm7 $&$ 0.55\pm0.06 $&$ 1.6\pm0.5 $&$ 0.031\pm0.006$\\
- $\PBs \to \Pphi \mu \mu$ &$ (3.2\pm1.3)\times10^2 $&$ 6.2\pm2.1 $&$ 17\pm7 $&$ 0.33\pm0.12$\\
- signal swaps &$ (3.6\pm0.9)\times10^2 $&$ 6.9\pm0.6 $&$ 33\pm9 $&$ 0.64\pm0.06$ \\
- $\PBd \to \PKstar \PJpsi$ swaps &$ (1.3\pm0.4)\times10^2 $&$ 2.6\pm0.4 $&$ 2.7\pm2.8 $&$ 0.05\pm0.05$ \\
-
- \hline
- \end{tabular}
- \end{tiny}
- \includegraphics[angle=-90,width=0.49\textwidth]{{images/h_Bd_Kstmm_vetoes}.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{{h_Lb_L1520mm_vetoes}.pdf}
-
- \end{center}
-
-
-
-
- \end{footnotesize}
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- \fi
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Multivariate simulation}
- {~}
- \begin{minipage}{\textwidth}
- \begin{columns}
-
- \column{0.5\textwidth}
- \begin{itemize}
- \begin{footnotesize}
- \item PID, kinematics and isolation variables used in a Boosted Decision Tree (BDT) to discriminate signal and background.
- \item BDT with k-Folding technique.
- \item Completely data driven.
- \end{footnotesize}
- \end{itemize}
- \begin{footnotesize}
- \begin{exampleblock}{}
- The k-Folding became a standard in LHCb
- \end{exampleblock}
- \end{footnotesize}
-
- \begin{center}
- \includegraphics[width=0.70\textwidth]{images/Chopping_Distrib.pdf}
- \end{center}
-
- \column{0.5\textwidth}
-
- \includegraphics[angle=-90,width=0.82\textwidth]{images/Fig1.pdf} \\
- \includegraphics[width=0.88\textwidth]{images/fold.png}
-
- \end{columns}
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Multivariate simulation, efficiency}
- {~}
-
- \begin{minipage}{\textwidth}
- \begin{footnotesize}
-
- \ARROW BDT was also checked in order not to bias our angular distribution:
- \begin{center}
- \includegraphics[angle=-90,width=0.8\textwidth]{images/BDT_Eff_Comp.pdf}
- \end{center}
- \ARROW The BDT has small impact on our angular observables. We will correct for these effects later on.
-
- \end{footnotesize}
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- \iffalse
- \begin{frame}{Mass modelling}
- {~}
- \begin{minipage}{\textwidth}
- \begin{tiny}
- \begin{columns}
- \column{0.1in}
- {~}
- \column{2.5in}
- \ARROW The signal is modelled by a sum of two Crystal-Ball functions with common mean.\\
- \ARROW The background is a single exponential.\\
- \ARROW The base parameters are obtained from the proxy channel: $\PBd \to \PJpsi (\mu\mu) \PKstar$.\\
- \ARROW All the parameters are fixed in the signal pdf.\\
- \ARROW Scaling factors for resolution are determined from MC.\\
- \ARROW In fitting the rare mode only the signal, background yield and the slope of the exponential is left floating.\\
- \begin{center}
- \includegraphics[angle=-90,width=0.9\textwidth]{images/msignal.pdf}\\
-
- \end{center}
- \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 $\left[ 1.1, 19.\right]~\GeV^2/c^4$.
- \column{2.5in}
- \includegraphics[angle=-90,width=0.95\textwidth]{{images/FitJpsiKstar_withBDT_withoutPartially}.pdf}\\
- \includegraphics[angle=-90,width=0.95\textwidth]{{images/Scaling_factor}.pdf}\\
- \ARROW The S-wave fraction is extracted using a \texttt{LASS} model.
- \end{columns}
-
- \end{tiny}
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Monte Carlo corrections}
- {~}
- \begin{minipage}{\textwidth}
- \begin{footnotesize}
- \ARROW No Monte Carlo simulation is perfect! One needs to correct for remaining differences.\\
- \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.
- \only<1>{
- \begin{center}
- \includegraphics[angle=-90,width=0.38\textwidth]{images/pt.pdf}
- \includegraphics[angle=-90,width=0.38\textwidth]{images/vertex.pdf}\\
- \includegraphics[angle=-90,width=0.38\textwidth]{images/nTracks.pdf}
- \end{center}
- }
- \only<2>{
- \begin{center}
- \includegraphics[angle=-90,width=0.38\textwidth]{images/eta_logy.pdf}
- \includegraphics[angle=-90,width=0.38\textwidth]{images/B0_p.pdf} \\
- \includegraphics[angle=-90,width=0.38\textwidth]{{images/bdt_data_mc_nominalMkpi}.pdf}
- \end{center}
- }
-
- \end{footnotesize}
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
- \fi
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Detector acceptance}
- {~}
- \begin{minipage}{\textwidth}
- \begin{footnotesize}
-
- \begin{columns}
-
- \column{0.6\textwidth}
- \begin{itemize}
- \item Detector distorts our angular distribution.
- \item We need to model this effect.
- \item 4D function is used:
- \begin{align*}
- \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),
- \end{align*}
- where $P_i$ is the Legendre polynomial of order $i$.
- \item We use up to $4^{th}, 5^{th}, 6^{th}, 5^{th}$ order for the $\cos \thetal, \cos \thetak, \phi, q^2$.
- \item The coefficients were determined using Method of Moments, with a huge simulation sample.
- \item The simulation was done assuming a flat phase space and reweighing the $q^2$ distribution to make is flat.
- \item To make this work the $q^2$ distribution needs to be reweighted to be flat.
- \end{itemize}
- %\includegraphics[width=0.75\textwidth]{images/q2PHSP.png}
-
-
-
- \column{0.4\textwidth}
- %\only<1>{
- %\includegraphics[width=0.99\textwidth]{images/q2PHSP.png}\\
- %\includegraphics[width=0.99\textwidth]{images/q2PHSPw.png}
- %}
-
- \only<1>{
- \includegraphics[width=0.99\textwidth]{images/det.png}
- }
- \end{columns}
-
-
- \end{footnotesize}
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Control channel}
- {~}
- \begin{minipage}{\textwidth}
- \begin{footnotesize}
- \begin{itemize}
- \item We tested our unfolding procedure on $\PB \to \PJpsi \PKstar$.
- \item The result is in perfect agreement with other experiments and our different analysis of this decay.
- \end{itemize}
- \end{footnotesize}
- \begin{center}
- \includegraphics[angle=-90,width=0.4\textwidth]{images/mlogjpsi.pdf}
- \includegraphics[angle=-90,width=0.4\textwidth]{images/mkpijpsi.pdf}\\
- \includegraphics[width=0.99\textwidth]{images/angles3.png}
- \end{center}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{The columns of New Physics}
- {~}
- \begin{minipage}{\textwidth}
- \begin{center}
- \includegraphics[width=0.94\textwidth]{images/columns.png}
-
- \end{center}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{The columns of New Physics}
- {~}
- \begin{minipage}{\textwidth}
- \begin{enumerate}
- \item Maximum likelihood fit:
- \begin{itemize}
- \item The most standard way of obtaining the parameters.
- \item Suffers from convergence problems, under coverages, etc. in low statistics.
- \end{itemize}
- \item Method of moments:
- \begin{itemize}
- \item Less precise then the likelihood estimator ($10-15\%$ larger uncertainties).
- \item Does not suffer from the problems of likelihood fit.
- \end{itemize}
- \item Amplitude fit:
- \begin{itemize}
- \item Incorporates all the physical symmetries inside the amplitudes! The most precise estimator.
- \item Has theoretical assumptions inside!
- \end{itemize}
- \end{enumerate}
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Maximum likelihood fit - Results}
- {~}
- \begin{footnotesize}
-
- \begin{minipage}{\textwidth}
- \ARROW In the maximum likelihood fit one could weight the events accordingly to the $\dfrac{1}{\varepsilon(\cos \thetal, \cos \thetak, \phi, q^2)}$\\
- \ARROW Better alternative is to put the efficiency into the maximum likelihood fit itself:
- \begin{align*}
- \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
- \end{align*}
- \ARROW Only the relative weights matters!\\
- \ARROW The Procedure was commissioned with TOY MC study.\\
- \ARROW Use Feldmann-Cousins to determine the uncertainties. \\
- \ARROW Angular background component is modelled with $2^{\rm nd }$ order Chebyshev polynomials, which was tested on the side-bands.\\
- \ARROW S-wave component treated as nuisance parameter.\\
- \includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_Afb3}.pdf}
- \includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P11}.pdf}
- \includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P57}.pdf}
-
- \end{minipage}
- \end{footnotesize}
- \vspace*{2.1cm}
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Maximum likelihood fit - Results}
- {~}
- \begin{minipage}{\textwidth}
- \begin{center}
- \only<1>{
- \includegraphics[angle=-90,width=0.49\textwidth]{images/FLPad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/S3Pad.pdf}\\
- \includegraphics[angle=-90,width=0.49\textwidth]{images/S4Pad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/S5Pad.pdf}
- }
- \only<2>{
- \includegraphics[angle=-90,width=0.49\textwidth]{images/AFBPad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/S7Pad.pdf}\\
- \includegraphics[angle=-90,width=0.49\textwidth]{images/S8Pad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/S9Pad.pdf}
- }
-
-
- \end{center}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Maximum likelihood fit - Results}
- \begin{minipage}{\textwidth}
- \begin{center}
- \includegraphics[angle=-90,width=0.65\textwidth]{images/P5pPadOverlay.pdf}\\
- \end{center}
-
- \begin{itemize}
- \item Tension with $3~\invfb$ gets confirmed!
- \item two bins both deviate by $2.8~\sigma$ from SM prediction.
- \item Result compatible with previous result.
- \end{itemize}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Method of moments}
- {~}
- \begin{footnotesize}
- \begin{minipage}{\textwidth}
- \begin{exampleblock}{}
- 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.\\
- \end{exampleblock}
- \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:
- \begin{align*}
- \int f_i(\overrightarrow{\Omega}) f_j(\overrightarrow{\Omega}) = \delta_{ij}
- \end{align*}
- \begin{align*}
- 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
- \end{align*}
- \ARROW Don’t have true angular distribution but we ''sample'' it with our data.\\
- \ARROW Therefore: $\int \to \sum$ and $M_i \to \widehat{M}_i$
- \begin{align*}
- \hat{M}_i=\dfrac{1}{\sum_e \omega_e} \sum_e \omega_e f_i(\overrightarrow{\Omega}_e)
- \end{align*}
- \ARROW The weight $\omega$ accounts for the efficiency. Again the normalization of weights does not matter.
-
-
- \end{minipage}
- \end{footnotesize}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- \begin{frame}{Method of moments - results}
- {~}
- \begin{footnotesize}
- \begin{minipage}{\textwidth}
-
- \only<3>
- {
- \begin{exampleblock}{}
- Method of Moments allowed us to measure for the first time a new observable:
- \end{exampleblock}
- }
-
- \begin{center}
- \only<1>{
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_FLPad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S3Pad.pdf}\\
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S4Pad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S5Pad.pdf}
- }
- \only<2>{
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_AFBPad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S7Pad.pdf}\\
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S8Pad.pdf}
- \includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S9Pad.pdf}
- }
- \only<3>{
- \includegraphics[angle=-90,width=0.75\textwidth]{images/S6cPad.pdf}
- }
-
- \end{center}
-
- \end{minipage}
- \end{footnotesize}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
-
- \begin{frame}{Amplitudes method}
- {~}
- \begin{footnotesize}
- \begin{minipage}{\textwidth}
-
- \ARROW Fit for amplitudes as (continuous) functions of $q^2$ in the region: $q^2 \in \left[ 1.1. 6.0 \right]~\GeV^2/c^4$.\\
- \ARROW Needs some Ansatz:
- \begin{align*}
- A(q^2) = \alpha + \beta q^2+ \dfrac{\gamma}{q^2}
- \end{align*}
- \ARROW The assumption is tested extensively with toys.\\
- \ARROW Set of 3 complex parameters $ \alpha, \beta, \gamma $ per vector amplitude:\begin{itemize}
- \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.
- \item Scalar amplitudes: $+4$ DoF.
- \item Symmetries of the amplitudes reduces the total budget to: $28$.
- \end{itemize}
- \ARROW The technique is described in \href{http://arxiv.org/pdf/1504.00574v2.pdf}{\color{blue}{JHEP06(2015)084}}.\\
- \ARROW Allows to build the observables as continuous functions of $q^2$:
- \begin{itemize}
- \item At current point the method is limited by statistics.
- \item In the future the power of this method will increase.
- \end{itemize}
- \ARROW Allows to measure the zero-crossing points for free and with smaller errors than previous methods.
- \end{minipage}
- \end{footnotesize}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- \begin{frame}{Amplitudes - results}
- {~}
- \begin{footnotesize}
- \begin{minipage}{\textwidth}
- \begin{center}
- \begin{columns}
- \column{0.45\textwidth}
- \includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_AFBOverlay}.pdf}\\
- \includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S4Overlay}.pdf}
-
- \column{0.45\textwidth}
- \includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S5Overlay}.pdf}\\
- {~}\\{~}\\{~}\\{~}\\
- \begin{large}
- Zero crossing points:
- \end{large}
- \begin{align*}
- q_0(S_4) & <2.65 & {\rm{~at~}} & 95\% ~CL \\
- q_0(S_5) & \in \left[ 2.49,3.95 \right] & {\rm{~at~}} & 68\% ~CL \\
- q_0(A_{FB}) & \in \left[ 3.40, 4.87 \right] & {\rm{~at~}} & 68\% ~CL
- \end{align*}
-
-
- \end{columns}
- \end{center}
-
- \end{minipage}
- \end{footnotesize}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
- \begin{frame}{Compatibility with SM}
- {~}
-
- \begin{minipage}{\textwidth}
-
- \begin{columns}
- \column{0.1in}
- {~}
- \column{2in}
- \ARROW Use \texttt{EOS} software package to test compatibility with SM.\\
- \ARROW Perform the $\chi^2$ fit to the measured:
- \begin{center}
- \begin{align*}
- F_L, A_{FB}, S_{3,..., 9} .
- \end{align*}
- \end{center}
- \ARROW Float a vector coupling: $\Re(C_9)$.\\
- \ARROW Best fit is found to be $3.4~\sigma$ away from the SM.
-
-
- \column{3in}
- \begin{align*}
- \Delta \Re (C_9) \equiv \Re(C_9)^{{\rm fit}} - \Re(C_9)^{{\rm SM}} = -1.03
- \end{align*}
- \includegraphics[angle=-90,width=0.95\textwidth]{images/wilsonchi2.pdf}
- \end{columns}
-
-
-
- \end{minipage}
-
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- \begin{frame}
- \begin{center}
- \begin{huge}
-
- Measurement of Higher $\PKstar$ states\\ in Electroweak Penguin decays
-
- \end{huge}
- \end{center}
- \end{frame}
-
-
-
- \begin{frame}\frametitle{$\PB \to \PKstar(1430) \Pmu \Pmu$}
- \begin{minipage}{\textwidth}
- {~}\\
- \ARROW If the NP effects the present in the $\PB \to \PKstar \Pmu \Pmu$ there is no reason why this should not appear in the higher resonances.\\
- \ARROW One the $m_{\PK \Ppi}$ spectrum: $1330 < m_{\PK \Ppi} < 1530~\MeV/c^2$.\\
- \ARROW Variety of states in that region: $\PKstar(1410)$, $\PKstar_0(1430)$, $\PKstar_2(1430)$.\\
- %\ARROW D-wave needs to be included in the moments analysis.\\
- \ARROW
- {~}\\
- \includegraphics[width=0.45\textwidth]{images/mkpi.png}
- \includegraphics[width=0.5\textwidth]{images/brk1430.png}
-
- \begin{exampleblock}{}
- First observation of this decay!
-
- \end{exampleblock}
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- \begin{frame}\frametitle{$\PB \to \PKstar(1430) \Pmu \Pmu$}
- \begin{minipage}{\textwidth}
- {~}\\
- \ARROW D-wave needs to be included in the moments analysis.\\
- \ARROW You end up with 42 angular coefficients...\\
- \ARROW With current statistics only Method of Moments can handle this.\\
- {~}\\
- \includegraphics[width=0.45\textwidth]{images/Fig6a.png}
- \includegraphics[width=0.5\textwidth]{images/Fig6b.png}
-
- \begin{exampleblock}{}
- First angular analysis!\\
- Theory predictions in behind.
-
- \end{exampleblock}
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
-
-
-
-
-
-
-
-
- \begin{frame}{Link the observables}
- \begin{footnotesize}
-
- \ARROW Fits prepare by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}, \href{http://arxiv.org/abs/1510.04239}{\color{blue}{arXiv::1510.04239}}
-
- \begin{itemize}
-
- \item Inclusive
-
- \begin{itemize}
- \item $B\to X_s\gamma$ {\color{gray}($BR$)
- .......................................................... } {\color{red} $\C7^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
- \item $B\to X_s\ell^+\ell^-$ {\color{gray}($dBR/dq^2$)
- ............................................ } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
- \end{itemize}
-
- \item Exclusive leptonic
-
- \begin{itemize}
- \item $B_s\to \ell^+\ell^-$ {\color{gray}($BR$)
- ........................................................ } {\color{red} $\C{10}^{(\prime)}$}
- \end{itemize}
-
- \item Exclusive radiative/semileptonic
- \begin{itemize}
- \item $B\to K^*\gamma$ {\color{gray}($BR$, $S$, $A_I$)
- ................................................ } {\color{red} $\C7^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
-
- \item $B\to K\ell^+\ell^-$ {\color{gray}($dBR/dq^2$)
- .............................................. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
-
- \item $\bf \color{Red} B\to K^*\ell^+\ell^-$ {\color{gray}($dBR/dq^2$, {\bf Optimized Angular Obs.})
- .. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
-
- \item $B_s\to \phi \ell^+\ell^-$ {\color{gray}($dBR/dq^2$, Angular Observables)
- .............. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
-
- \item $\Lambda_b\to \Lambda\ell^+\ell^-$ {\color{gray}(None so far)}
- \item etc.
- \end{itemize}
-
-
-
- \end{itemize}
- \end{footnotesize}
-
- \end{frame}
-
- \frame{ \frametitle{Statistic details}
-
- \begin{footnotesize}
-
- \ARROW Frequentist approach:
- \medskip
-
- $$\chi^2(C_i) = [O_\text{exp}- O_\text{th}(C_i)]_j \, [Cov^{-1}]_{jk}\, [O_\text{exp}- O_\text{th}(C_i)]_k$$
-
-
- \begin{itemize}
- \item $\bf Cov = Cov^\text{exp} + Cov^\text{th}$. We have $Cov^\text{exp}$ for the first time
- \item Calculate $Cov^\text{th}$: correlated multigaussian scan over all nuisance parameters
- \item $Cov^\text{th}$ depends on $C_i$: Must check this dependence\\[5mm]
- \end{itemize}
- For the Fit:
- \begin{itemize}
- \item Minimise $\chi^2 \to \chi^2_\text{min} = \chi^2(C_i^0)\quad$ (Best Fit Point = $C_i^0$)
- \item Confidence level regions: $\chi^2(C_i) - \chi^2_\text{min} < \Delta\chi_{\sigma,n}$
- %\item Compute pulls by inversion of the above formula
- \end{itemize}
- \medskip
- \ARROW The results from 1D scans:{~}\\{~}\\
- \begin{tiny}
- \begin{tabular}{crccc}
- %\toprule[1.6pt]
- Coefficient ${\cal C}_i^{NP}={\cal C}_i-{\cal C}_i^{SM}$ & Best fit & 1$\sigma$ & 3$\sigma$ & Pull$_{\rm SM}$ \\ \hspace{10mm} \\[5mm]
- % \midrule
- $\bf\cred\C9^{\rm NP}$ & $ -1.09 $ & $ [-1.29,-0.87] $ & $ [-1.67,-0.39] $ & $\,\,\,\,\,\,\bf 4.5
- \cred \Leftarrow$ \hspace{5mm} \\[3mm]
- $\C9^{\rm NP}=-\C{10}^{\rm NP}$ & $ -0.68 $ & $ [-0.85,-0.50] $ & $ [-1.22,-0.18] $ & \bf \quad 4.2
- $\cred\Leftarrow$ \hspace{5mm} \\[3mm]
- $\C9^{\rm NP}=-\C{9'}^{\rm NP}$ & $ -1.06 $ & $ [-1.25,-0.86] $ & $ [-1.60,-0.40] $ & \quad \quad \quad \,\,\quad 4.8
- $\cred\Leftarrow$ (no $R_K$)\hspace{5mm} \\[3mm]
-
- \hspace{5mm} \\[3mm]
- % \bottomrule[1.6pt]
- \end{tabular}
- \end{tiny}
- \end{footnotesize}
-
- }
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Theory implications}
- {~}
- \begin{minipage}{\textwidth}
-
- \begin{itemize}
- \item The data can be explained by modifying the $C_9$ Wilson coefficient.
- \item Overall there is around $4.5~\sigma$ discrepancy wrt. SM.
- \end{itemize}
- \includegraphics[width=0.9\textwidth]{images/C9.png}
-
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- \begin{frame}{2D scans}
- {~}
- \begin{footnotesize}
-
- \begin{minipage}{\textwidth}
- \begin{columns}
- \begin{column}{0.5cm}
-
-
- \end{column}
- \begin{column}{17cm}
-
- \renewcommand{\arraystretch}{1.4}
- \setlength{\tabcolsep}{13pt}
- \begin{tabular}{cccr}
- \hline
- Coefficient & Best Fit Point & Pull$_{\rm SM}$ \\ \hline
-
- $(\C7^{\rm NP},\C9^{\rm NP})$ & $(-0.00,-1.07)$ & {\bf 4.1} \hspace{5mm} \\
- $(\C9^{\rm NP},\C{10}^{\rm NP})$ & $(-1.08,0.33)$ & {\bf 4.3} \hspace{5mm} \\
- $(\C9^{\rm NP},\C{7'}^{\rm NP})$ & $(-1.09,0.02)$ & {\bf 4.2} \hspace{5mm} \\
- $(\C9^{\rm NP},\C{9'}^{\rm NP})$ & $(-1.12,0.77)$ & {\bf 4.5} \hspace{5mm} \\
- $(\C9^{\rm NP},\C{10'}^{\rm NP})$ & $(-1.17,-0.35)$ & {\bf 4.5} \hspace{5mm} \\
- $(\C{9}^{\rm NP}=-\C{9'}^{\rm NP},\C{10}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-1.15,0.34)$ & \!\!\!\!\!\!\!\!\!\!\! {\bf 4.7} \\
- $(\C{9}^{\rm NP}=-\C{9'}^{\rm NP},\C{10}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-1.06,0.06)$ & {\bf 4.4} \hspace{5mm} \\
- $(\C{9}^{\rm NP}=\C{9'}^{\rm NP},\C{10}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-0.64,-0.21)$ & 3.9 \hspace{5mm} \\
- $(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-0.72,0.29)$ & 3.8 \hspace{5mm} \\
- % $(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-0.66,0.03)$ & 2.0 & 23.0
- %$(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-0.69,0.05)$ & 1.9 & 22.0 \hspace{5mm} \\
-
- \end{tabular}
- \end{column}
- \end{columns}
-
-
- \medskip
- \begin{itemize}
- \item $C_9^{NP}$ always play a dominant role
- \item All 2D scenarios above 4$\sigma$ are quite indistinguishable. We have done a systematic study to check
- what are the most relevant Wilson Coefficients to explain all deviations, by allowing progressively different WC to get NP contributions and comparing the pulls.
-
-
- \end{itemize}
-
-
-
- \end{minipage}
-
- \end{footnotesize}
- \vspace*{2.1cm}
- \end{frame}
-
- %%%%%%%%%%%%%%%%%
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{If not NP?}
- {~}
- \begin{minipage}{\textwidth}
- \begin{itemize}
- \item We are not there yet!
- \item There might be something not taken into account in the theory.
- \item Resonances ($\PJpsi$, $\Ppsi(2S)$) tails can mimic NP effects.
- \item There might be some non factorizable QCD corrections.\\
- '' 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}
- .
- \end{itemize}
- \only<1>{
- \begin{center}
-
- \includegraphics[width=0.9\textwidth]{images/QCDSHIT.png}
- \end{center}
- }
- \only<2>{
- \begin{center}
- \includegraphics[width=0.6\textwidth]{images/charmloop2.png}
- \end{center}
- }
- \only<3>{
- \begin{center}
- \includegraphics[width=0.6\textwidth]{images/charmloop3.png}
- \end{center}
- }
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- % Why flavour physics
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- \begin{center}
- \begin{Huge}
- Disclaimers about some theory predictions
- \end{Huge}
- \end{center}
-
-
-
-
- \end{frame}
-
-
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Disclaimer 1 }
- {~}
-
-
-
- \begin{minipage}{\textwidth}
- \ARROW \href{http://arxiv.org/abs/1512.07157}{\color{blue}{arXiv:1512.07157}}, Ciuchini, Fedele, Franco, Mishima, Paul, Silvestrini, Valli\\
- \begin{itemize}
- \item Introduce a fully arbitrary parametrization for non-factorizable power correction:
- \begin{align*}
- \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}
- \end{align*}
- with ($\lambda=0,\pm$)\hfill(copied from JC'14).\\
- {\bf Complications:} complete lack of theory input/output $\Rightarrow$ {\bf no predictivity} with 18 free parameters (any shape). Specific problems...
-
- \item Because of the polynomial parametrization this is completely unphysical as it will never reproduce the amplitudes that where measured at the $B \to K^{\ast} \PJpsi$.
-
-
- \end{itemize}
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- \begin{frame}{Disclaimer 1 }
- {~}
- \begin{minipage}{\textwidth}
- \ARROW If one put some physics in their complete random parametrization.\\
- \ARROW For example at the $m_{\PJpsi}$ and $m_{\Ppsi(2S)}$ it has to reproduce the Babar, Belle, LHCb.\\
- \begin{exampleblock}{}
- \texttt{arXiv:1512.XXXX}, C.Bobeth, M.Chrzaszcz, D. van Dyk, J.Virto
- \end{exampleblock}
- \begin{center}
- \includegraphics[width=0.65\textwidth]{{images/fig-btokstarll-p5prime}.pdf}
- \end{center}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}\frametitle{Disclaimer 2}
- \ARROW arXiv::1603.04355
- \begin{center}
- \includegraphics[width=0.9\textwidth]{images/NP.png}
- \end{center}
- \only<2>{
- \includegraphics[width=0.55\textwidth]{images/rahul.png}
- }
-
-
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}\frametitle{Disclaimer 2}
- \ARROW arXiv::1603.04355
- \begin{columns}
- \column{0.1in}
- {~}
- \column{3in}
- \ARROW ''{\it The relation in Eq. (24) between form factors is expected to be satisfied in the large $q^2$ region. Eq. (24) is naturally satisfied if it is valid at each order in the Taylor expansion of the form factors}''\\
- \ARROW They need Eq. 24 to be valid with at least leading order at the Taylor expansion.\\
- \ARROW But this is not guaranteed as a resonant contribution can violate this expression.\\
- \ARROW Futhermore the width of the of the $\PKstar$ screws up totally the end-points relations.
- \column{2in}
- \includegraphics[width=0.9\textwidth]{images/mist.png}\\
- \includegraphics[width=0.9\textwidth]{images/reson.png}\\
-
- \end{columns}
- \includegraphics[angle=-90,width=0.4\textwidth]{{images/ForTom_Q2_FLATQ2_Kmumu}.pdf}
- \includegraphics[angle=-90,width=0.4\textwidth]{{images/ForTom_Q2_FLATQ2}.pdf}
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Conclusions}
- {~}
- \begin{minipage}{\textwidth}
- \begin{itemize}
- \item Enormous NP program searched performed!
- \item Clear tensions wrt. SM predictions!
- \item Measurements cluster in the same direction.
- \item We are not opening the champagne yet!
- \item Still need improvement both on theory and experimental side.
- \item Time will tell if this is QCD+fluctuations or new Physics:
- \end{itemize}
- \pause
- ... when you have eliminated all the\\
- Standard Model explanations, whatever remains,\\
- however improbable, must be New Physics.\\
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- {~}
- \begin{minipage}{\textwidth}
- \begin{center}
- \begin{LARGE}
- Thank you for the attention!
- \end{LARGE}
- \includegraphics[width=0.8\textwidth]{images/Joke.jpg}
-
- \end{center}
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- \backupbegin
-
- \begin{frame}\frametitle{Backup}
-
-
- \end{frame}
-
- \begin{frame}
- \begin{center}
- \includegraphics[width=0.9\textwidth]{images/criv.png}
- \end{center}
-
-
- \ARROW Stolen from A.Crivelin
- \end{frame}
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- \begin{center}
- \begin{Huge}
- Other related LHCb measurements.
-
- \end{Huge}
- \end{center}
-
-
-
-
- \end{frame}
-
-
-
-
-
-
-
-
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Branching fraction measurements of $\PB \to \PKstar^{\pm} \Pmu \Pmu$}
- {~}
- \includegraphics[width=0.5\textwidth]{images/ksmumu_BF.png}
- \includegraphics[width=0.5\textwidth]{images/kmumu_BF.png}
-
- \begin{center}
- \begin{columns}
-
- \column{0.4\textwidth}
- \begin{itemize}
- \item Despite large theoretical errors the results are consistently smaller than SM prediction.
- \end{itemize}
- \column{0.6\textwidth}
- \includegraphics[width=0.87\textwidth]{images/bukst_BF.png}
-
-
- \end{columns}
-
-
-
-
-
-
-
- \end{center}
- \vspace*{2.1cm}
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Branching fraction measurements of $\PBs \to \Pphi \Pmu \Pmu$}
- {~}
- \begin{minipage}{\textwidth}
- \begin{center}
- \includegraphics[width=0.65\textwidth]{images/bs2phipi.png}\\
- \end{center}
-
- \begin{itemize}
- \item Recent LHCb measurement [JHEPP09 (2015) 179].
- \item Suppressed by $\frac{f_s}{f_d}$.
- \item Cleaner because of narrow $\Pphi$ resonance.
- \item $3.3~\sigma$ deviation in SM in the $1-6\GeV^2$ bin.
- \end{itemize}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Branching fraction measurements of $\PLambdab \to \PLambda \Pmu \Pmu$}
- {~}
- \begin{minipage}{\textwidth}
-
- \begin{center}
- \only<1>{
- \includegraphics[width=0.65\textwidth]{images/Lb_BR.png}
- }
- \only<2>{
- \includegraphics[width=0.45\textwidth]{images/Lblow.png}
- \includegraphics[width=0.45\textwidth]{images/Lbhigh.png}
-
- }
-
-
- \end{center}
-
-
- \begin{itemize}
- \item This years LHCb measurement [JHEP 06 (2015) 115]].
- \item In total $\sim 300$ candidates in data set.
- \item Decay not present in the low $q^2$.
-
- \end{itemize}
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- \begin{frame}{Angular analysis of $\PLambdab \to \PLambda \Pmu \Pmu$}
- {~}
- \begin{minipage}{\textwidth}
-
- \begin{itemize}
- \item For the bins in which we have $>3~\sigma$ significance the forward backward asymmetry for the hadronic and leptonic system.
- \end{itemize}
- \begin{center}
- \includegraphics[width=0.9\textwidth]{{images/AFB_Lb}.png}
- \end{center}
- \begin{itemize}
- \item $A_{FB}^H$ is in good agreement with SM.
- \item $A_{FB}^{\ell}$ always in above SM prediction.
- \end{itemize}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Lepton universality test}
- {~}
- \begin{minipage}{\textwidth}
- \begin{columns}
- \column{3.0in}
- \begin{itemize}
- \item If $\PZprime$ is responsible for the $P'_5$ anomaly, does it couple equally to all flavours?
- \includegraphics[width=0.9\textwidth]{images/uni2.png}
- \item Challenging analysis due to bremsstrahlung.
- \item Migration of events modeled by MC.
- \item Correct for bremsstrahlung.
- \item Take double ratio with $\PBplus \to \PJpsi \PKplus$ to cancel systematics.
- \item In $3\invfb$, LHCb measures $R_K=0.745^{+0.090}_{-0.074}(stat.)^{+0.036}_{-0.036}(syst.)$
- \item Consistent with SM at $2.6\sigma$.
-
- \end{itemize}
- \column{2.0in}
- \includegraphics[width=0.99\textwidth]{images/RK.png}\\
- \begin{itemize}
- \item \href{http://arxiv.org/abs/1406.6482}{Phys. Rev. Lett. 113, 151601 (2014)}
- \end{itemize}
- \end{columns}
-
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{Angular analysis of $\PBzero \to \PKstar \Pe \Pe$}
- {~}
- \only<1>{
- \begin{minipage}{\textwidth}
- \begin{itemize}
- \item With the full data set ($3\invfb$) we performed angular analysis in $0.0004 < q^2 <1~\GeV^2$.
- \item Electrons channels are extremely challenging experimentally:
- \begin{itemize}
- \item Bremsstrahlung.
- \item Trigger efficiencies.
- \end{itemize}
- \item Determine the angular observables: $\FL$, $\ATD$, $\ATRe$, $\ATIm$:
- \end{itemize}
- \begin{equation}
- \label{eq:physPars}
- \begin{split}
- \FL &=\frac{|A_0|^2}{|A_0|^2+|A_{||}|^2 + |A_\perp|^2}\\
- \ATD &= \frac{|A_\perp|^2-|A_{||}|^2}{|A_\perp|^2+|A_{||}|^2}\\
- \ATRe &= \frac{2\Real(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2}\\
- \ATIm &= \frac{2\Imag(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2},
- \end{split}\nonumber
- \end{equation}
-
- \end{minipage}
- }
- \only<2>{
- \begin{center}
- \includegraphics[width=0.5\textwidth]{images/Kstee.png}\\
- \end{center}
- \begin{itemize}
- \item Results in full agreement with the SM.
- \item Similar strength on $C_7$ Wilson coefficient as from $\Pbeauty \to \Pstrange \Pphoton$ decays.
- \end{itemize}
-
- \begin{center}
- \includegraphics[width=0.9\textwidth]{images/Kstee2.png}
- \end{center}
-
- }
- \vspace*{2.1cm}
- \end{frame}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{There is more!}
- {~}
- \begin{minipage}{\textwidth}
-
- \begin{itemize}
- \item There is one other LUV decay recently measured by LHCb.
- \item $R(\PDstar)=\dfrac{\mathcal{B}(\PB \to \PDstar \Ptau \Pnu)}{\mathcal{B}(\PB \to \PDstar \Pmu \Pnu)}$
- \item Clean SM prediction: $R(\PDstar)=0.252(3)$, PRD 85 094025 (2012)
- \item LHCb result: $R(\PDstar)= 0.336 \pm 0.027 \pm 0.030$, HFAG average: $R(\PDstar)=0.322 \pm 0.022$
- \item $3.9~\sigma$ discrepancy wrt. SM prediction
- \end{itemize}
-
- \begin{center}
-
- \includegraphics[width=0.52\textwidth]{images/RDstar.png}
-
- \end{center}
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
- \begin{frame}
- \begin{center}
- \begin{Huge}
- Global fit to $\Pbeauty \to \Pstrange \ell \ell$ measurements
- \end{Huge}
- \end{center}
-
-
-
-
- \end{frame}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$ kinematics}
- {~}
- \begin{minipage}{\textwidth}
-
- $\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.
-
- \only<1>{
- \begin{columns}
- \column{0.5\textwidth}
-
- $\color{JungleGreen}{\Rrightarrow}$ $\cos \thetak$: 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.\\
- $\color{JungleGreen}{\Rrightarrow}$ $\cos \thetal$: 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.\\
- $\color{JungleGreen}{\Rrightarrow}$ $\phi$: the angle between the plane containing the $\Pmuon$ and $\APmuon$ and the plane containing the kaon and pion from the $\PKstar$.
-
-
-
- \column{0.5\textwidth}
- \includegraphics[width=0.95\textwidth]{images/angles.png}
-
- \end{columns}
- }
- \only<2>{
- {\tiny{
- \eqa{\label{dist}
- \frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi}&=&\frac9{32\pi} \bigg[
- 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]
- &&\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]
- &&\hspace{-2.7cm}+ (J_{6s} \sin^2\theta_K + {J_{6c} \cos^2\theta_K}) \cos\theta_l
- + 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]
- &&\hspace{-2.7cm}+ J_9 \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,,
- \nonumber}
- }}
- $\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decay.
-
- }
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
- \begin{frame}\frametitle{Backup}
-
- \ARROW ves:
- \begin{align*}
- \langle H \rangle = \frac{1}{\sqrt{2}}\begin{pmatrix}
- 0\\
- \nu
- \end{pmatrix}\\
- \langle S \rangle = x.
- \end{align*}
-
-
- \ARROW Minimalization:
- \begin{align*}
- 0 = -\mu^2 + \lambda_H \nu^2 + a_1 x^2 + \frac{1}{2} x^2\\
- 0 = b_2 + b_3 x+ b_4 x^2 + \frac{a_1\nu^2}{4 x_0} + \frac{a_2 \nu_0^2}{2}
- \end{align*}
-
- \end{frame}
-
-
-
-
- \begin{frame}\frametitle{Backup}
-
- \ARROW generate the mass:
- \begin{align*}
- \mathcal{L}_{mass}=-\frac{1}{2}
- \begin{pmatrix}
- h \\
- s
- \end{pmatrix}^T
- \begin{pmatrix}
- A & C \\
- C & B
- \end{pmatrix}
- \begin{pmatrix}
- s^{\prime}\\
- h^{\prime}
- \end{pmatrix}
- \end{align*}
-
- \begin{align*}
- \cos \theta = 2(1+y^{-2}(1-\sqrt{1+y^2}))^{-0.5}\\
- \sin \theta = 2(1+y^{-2}(1+\sqrt{1+y^2}))^{-0.5}\\
- y=\frac{2C}{A-B}
- \end{align*}
- \ARROW Mass eigenvalues:
- \begin{align*}
- m^2_{h^{\prime}/s^{\prime}} = \frac{1}{2}\left[A + B \pm (A-B)\sqrt{1+y^2}\right]
- \end{align*}
-
- \end{frame}
-
-
-
- \begin{frame}\frametitle{Naturalnes}
-
- \ARROW If the $\sin \theta \ll 1$
- \begin{align*}
- m^2_{h^{\prime}} \sim 2 \lambda_H \nu^2\\
- m^2_{s^{\prime}} \sim b_3 x + 2b_4 x^2 -\frac{a_1\nu^2}{4 x}
- \end{align*}
- \ARROW Since Higgs is $125\GeV$ then $m_S \sim \mathcal{O}(1)$
-
- \end{frame}
-
- \begin{frame}[c]{The inflaton model}
- \begin{minipage}{\textwidth}
- \begin{small}
- \ARROW The model is extremely simple:
- \begin{align*}
- V(H,S)=V_H + V_{\rm mix} + V_S,
- \end{align*}
- where
- \begin{align*}
- V_H = -\mu^2 H^{\dag}H + \lambda_H (H^{\dag} H)^2\\
- V_{\rm mix} = \frac{a_1}{2}\left(H^{\dag}H\right)S + \frac{a_2}{2}\left(H^{\dag}H\right)S^2\\
- V_S = \frac{b_2}{2}S^2 + \frac{b_3}{3}S^3 + \frac{b_4}{4}S^4
- \end{align*}
- \ARROW Now the Lagrangian needs to be written in physical degrees of freedom:
- \begin{itemize}
- \item You start by minimizing the scalar potential.
- \item Then you expand the group states (linear terms in h, s expansion vanish).
- \item Then you generate the mass is given(see backup for details):
- \end{itemize}
- \begin{align*}
- \mathcal{L}_{mass}=-\frac{1}{2}
- \begin{pmatrix}
- h \\
- s
- \end{pmatrix}^T
- \begin{pmatrix}
- A & C \\
- C & B
- \end{pmatrix}
- \begin{pmatrix}
- s^{\prime}\\
- h^{\prime}
- \end{pmatrix}
- \end{align*}
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
- \begin{frame}[c]{The inflaton model}
- \begin{minipage}{\textwidth}{~}\\
- \begin{small}
- \ARROW You can diagonalize the matrix by orthogonal transformation:
- \begin{align*}
- \begin{pmatrix}
- h \\
- s
- \end{pmatrix}=
- \begin{pmatrix}
- \sin \theta & \cos \theta \\
- \cos \theta & \sin \theta
- \end{pmatrix}
- \begin{pmatrix}
- s^{\prime}\\
- h^{\prime}
- \end{pmatrix}
- \end{align*}
- where
- \begin{align*}
- \cos \theta = 1 +\mathcal{O}(y^2),~~
- \sin \theta = y + \mathcal{O}(y^3)~~
- y = \frac{2C}{A-B}
- \end{align*}
- \ARROW For small mixing:
- \begin{align*}
- m^2_{S^{\prime}} \sim B - \frac{1}{4}(A-B)y^2
- \end{align*}
- \ARROW So now comes something that is the most important; all the interaction with the SM is done just by assuming it's Higgs and inserting: $h \to \sin \theta s$
-
- \ARROW For example:
- \begin{align*}
- \mathcal{L}_Y = - m_f h \bar{\psi}_f \psi_f + {\rm h.c.}~~~~~\mapsto \mathcal{L}_{S^{\prime}ff}= - m_f \sin \theta s \bar{\psi}_f \psi_f + {\rm h.c.}
- \end{align*}
-
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
-
- \begin{frame}[c]{The inflaton model, so what?}
- \begin{minipage}{\textwidth}
- \begin{small}
- \ARROW For a given mixing angle $\sin \theta$ and the inflaton mass we can calculate it's width:
- \begin{align*}
- \Gamma_{\ell \ell} = \frac{\sin^2 \theta}{8 \pi \nu^2}m_{\ell}^2 m_S \left(1-\frac{4m^2_{\ell}}{m^2_S} \right)^{\frac{3}{2}}\\
- c \tau_S \approx 60 \times \left(\frac{0.01}{\sin \theta}\right)^2 \left(\frac{500}{m_S}\right)^3 \rm [mm]
- \end{align*}
-
- \ARROW Since in experiment we set limits in 2D space: $(m_S, c \tau_S)$ we can map it to: $(m_S, \sin \theta)$.\\
- \ARROW Now the misunderstanding started with ''Light inflaton Hunter's Guide'' D. Gorbunov:
- \begin{equation}
- {\rm Br} (\PB \to \chi X_s) ~\sim 10^{-6}\left(1-\frac{m^2_{\chi}}{m^2_b}\right) \left(\frac{\beta}{\beta_0}\right) \left(\frac{300{\rm MeV}}{m_{\chi}}\right)
- \end{equation}
- and:
- ''where Xs stands for strange meson channel mostly saturated by a sum of pseudoscalar and vector kaons.''
-
-
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
- \begin{frame}[c]{The inflaton model, so what?}
- \begin{minipage}{\textwidth}
- \begin{small}
- \ARROW In the interpretation of the $\PB \to \PKstar \xi$ they followed Gorbunov and assumed that the $33\%$ of $X_s$ are a $\PKstar$ and used the above formula.\\
- \ARROW We followed a different approach and calculated the exclusive widths:
- \begin{align*}
- \mathcal{M}=-\frac{1}{2}c_h \theta \langle K \vert \bar{s}b \vert B \rangle = -\frac{1}{2} c_h \theta \frac{M_B^2-M_K^2}{m_b-m_s} f_0(m_s^2)
- \end{align*}
- \begin{align*}
- \Gamma_{\PB \to \PKstar \chi} = \frac{c_h \theta^2}{64 \pi} \lambda^{1/2}(1,\frac{M_K^2}{M_B^2}, \frac{M_S^2}{M_B^2})f_0(m_S^2) \frac{(M_B^2 - M_K^2)}{M_B(m_b- m_s)^2}
- \end{align*}
-
- \ARROW Now after we calculate this our self we found the solution in the literature \href{http://journals.aps.org/prd/pdf/10.1103/PhysRevD.83.054005}{ B.Batel et. al}
-
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
- \begin{frame}[c]{The inflaton model, so what?}
- \begin{minipage}{\textwidth}
- \begin{small}
- {~}\\
- \ARROW Now if we look how many of the $X_s$ are $\PK$ and $\PKstar$ we define the variables:
- \begin{align*}
- r_K = \frac{\PB \to \PK \chi}{\PB \to X_s \chi}~~~~r_{\PKstar} = \frac{\PB \to \PKstar \chi}{\PB \to X_s \chi}
- \end{align*}
- \includegraphics[width=0.45\linewidth]{images/rk_graph.png}
- \includegraphics[width=0.45\linewidth]{images/rkstar.png} \\
- {~}\\
- \ARROW So the assumption about $33~\%$ was generous assumption.
-
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
- \begin{frame}[c]{Cross check of the calculations}
- \begin{minipage}{\textwidth}
- \begin{small}
- {~}\\
- \ARROW So we have cross-checked this calculations with old Higgs papers. \\
- \ARROW In the 80s they thought that Higgs might he light enough that it can be produced in $\PB$ decays.\\
- \ARROW From Haber, et al.:
- \begin{center}
- \includegraphics[width=0.45\textwidth]{images/higgs.png}
- \end{center}
- \ARROW So everything is consistent.
- \end{small}
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
-
- \begin{frame}{The result}
- \begin{minipage}{\textwidth}
-
-
- \begin{center}
- \includegraphics[angle=-90,width=0.9\textwidth]{{images/Inflaton_parameter_space_log}.pdf}
- \end{center}
-
-
- \end{minipage}
- \vspace*{2.cm}
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}{If not NP?}
- {~}
- \begin{minipage}{\textwidth}
- \begin{itemize}
- \item How about our clean $P_i$ observables?
- \item The QCD cancel as mentioned only at leading order.
- \item Comparison to normal observables with the optimised ones.
- \end{itemize}
- \includegraphics[width=0.9\textwidth]{images/C9_S_P.png}
-
-
- \end{minipage}
- \vspace*{2.1cm}
- \end{frame}
-
-
-
-
- \backupend
-
- \end{document}