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\usetheme{Sybila}
\title[Lepton Flavour Violation at LHCb ]{Lepton Flavour Violation at LHCb}
\author{Marcin Chrz\k{a}szcz$^{1,2}$ \\ \footnotesize{on behalf of the LHCb collaboration}}
\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow \\{~}\\ International Workshop on Tau Lepton Physics 2014,\\ Aachen, Germany }
\date{\today}
\begin{document}
% --------------------------- SLIDE --------------------------------------------
\frame[plain]{\titlepage}
\author{Marcin Chrz\k{a}szcz}
% ------------------------------------------------------------------------------
% --------------------------- SLIDE --------------------------------------------
\institute{~(UZH, IFJ)}
% \begin{frame}\frametitle{Outline}
% \begin{enumerate}
% \item introduction\vspace{.5em}
% \item multivariate technique\vspace{.5em}
% \item normalisation\vspace{.5em}
% % \item backgrounds\vspace{.5em}
% \item expected sensitivity\vspace{.5em}
% \item model dependence\vspace{.5em} data from Reco14Stripping20(r1)
% \end{enumerate}
% Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green}
% \end{frame}
\begin{frame}\frametitle{Outline}
\tableofcontents
\end{frame}
\section{LHCb detector}
\begin{frame}\frametitle{LHCb detector}
\begin{columns}
\column{3.in}
\begin{center}
\includegraphics[width=0.98\textwidth]{det.jpg}
\end{center}
\column{2.0in}
\begin{footnotesize}
LHCb is a forward spectrometer:
\begin{itemize}
\item Excellent vertex resolution.
\item Efficient trigger.
\item High acceptance for $\Ptau$ and $\PB$.
\item Great Particle ID
\end{itemize}
\end{footnotesize}
\end{columns}
\end{frame}
\section{Lepton Flavour Violation status}
\begin{frame}\frametitle{Lepton Flavour/Number Violation}
\begin{small}
Lepton Flavour Violation(LFV):
\end{small}
\begin{footnotesize}
After $\Pmuon$ was discovered (1936) it was natural to think of it as an excited $\Pelectron$.
\begin{columns}
\column{3in}
\begin{itemize}
\item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$
\item Unless another $\Pnu$, in intermediate vector boson loop, cancels.
\end{itemize}
\column{2in}
{~}\includegraphics[width=0.98\textwidth]{rabi.png}
\end{columns}
\begin{columns}
\column{0.5in}
{~}
\column{3in}
\begin{block}{I.I.Rabi:}
"Who ordered that?"
\end{block}
\column{0.3in}{~}
\column{2in}
{~}\includegraphics[scale=0.08]{II_Rabi.jpg}
\end{columns}
\begin{itemize}
\item Up to this day charged LFV is being searched for in various decay modes.
\item LFV was already found in neutrino sector (oscillations).
\end{itemize}
\end{footnotesize}
\begin{footnotesize}
\begin{columns}
\column{3.5in}
\begin{small}
Lepton Number Violation (LNV) (see J. Harrison \href{https://indico.cern.ch/event/300387/session/17/contribution/74}{\color{blue}talk})
\end{small}
\begin{itemize}
\item Even with LFV, lepton number can be a conserved quantity.
\item Many NP models predict it violation(Majorana neutrinos)
\item Searched in so called Neutrinoless double $\beta$ decays.
\end{itemize}
\column{1.5in}
\includegraphics[width=0.73\textwidth]{Double_beta_decay_feynman.png}
\end{columns}
\end{footnotesize}
%Double_beta_decay_feynman.png
% \textref{M.Chrz\k{a}szcz 2014}
\end{frame}
\begin{frame}
\frametitle{Status of $\color{white} \tau \to \mu \mu \mu$ in Tau 2012}
\begin{columns}
\begin{column}{.6\textwidth}
\begin{alertblock}{current limits ($ \color{white} 90\,\%$ CL)}
\begin{description}
\item[BaBar] $3.3\times 10^{-8}$
\item[Belle] $2.1\times 10^{-8}$
\item[LHCb] $8.0\times 10^{-8}~(1 \invfb)$
\end{description}
\end{alertblock}
{~}\\
\includegraphics[width=.95\textwidth]{TauLFV_UL_2013001_old.pdf}
\end{column}
\begin{column}{.4\textwidth}
\includegraphics[width=.45\textwidth]{275px-Nagoya_Castle.jpg}{~}
\includegraphics[width=.45\textwidth]{taushodo.jpg}\\{~}\\{~}\\
\includegraphics[width=.93\textwidth]{Fig3a.png}
\end{column}
\end{columns}
\begin{Large}
Today: Update with full LHCb data sample $(3\invfb)$!
\end{Large}
\end{frame}
\begin{frame}
\section{Selection}
\frametitle{Strategy}
\begin{itemize}
\item Blind analysis.
\item Loose selection.
\item Multivariate classification in: mass, PID($\mathcal{M}_{PID}$), geometry($\mathcal{M}_{3body}$).
\item Binning optimisation.
\item Consider 2012($8~\TeV$) and 2011($7~\TeV$) data separately.
\item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$).
\item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$.
\item ``middle sidebands'' for classifier evaluation and tests: ($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$).
\item CLs for limit calculation.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{$\color{white} \tau$ production}
\begin{itemize}
\item $\Ptau$'s in LHCb come from five main sources:
\end{itemize}
\begin{center}
\begin{tabular}{| c | c | c | }
\hline
Mode & $7~\TeV$ & $8~\TeV$ \\ \hline
Prompt $\PDs\to\Ptau$ & $71.1\pm3.0\,\%$ & $72.4\pm2.7\,\%$ \\
Prompt $\PDplus\to\Ptau$ & $4.1\pm0.8\,\%$ & $4.2\pm0.7\,\%$ \\
Non-prompt $\PDs\to\Ptau$ & $9.0\pm2.0\,\%$ & $8.5\pm1.7\,\%$ \\
Non-prompt $\PDplus\to\Ptau$ & $0.18\pm0.04\,\%$ & $0.17\pm0.04\,\%$ \\
$X_{\Pbottom}\to\Ptau$ & $15.5\pm2.7\,\%$ & $14.7\pm2.3\,\%$ \\ \hline
\end{tabular}
\end{center}
\begin{columns}
\column{0.8\textwidth}
\begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$}
\begin{itemize}
\item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$.
\item One can calculate it from: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space.
\item \texttt{hep-ex:0604043}.
\item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=(1.0\pm0.1) \times10^{-3}$.
\end{itemize}
\end{exampleblock}
\column{0.2\textwidth}
{~}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Triggers at LHCb}
\begin{itemize}
\item LHCb uses complex trigger\footnote{\href{http://arxiv.org/abs/1211.3055}{\color{blue}arxiv 1211.3055}}
\item $\mathcal{O}(100)$ trigger lines.
\item Lines change with data taking.
\item Optimized choice of triggers based on $\dfrac{s}{\sqrt{b}}$ FOM.
\item Evaluated different triggers used in 2012 data taking.
\item Found negligible differences in trigger efficiencies.
\end{itemize}
\end{frame}
\section{Multivariate technique}
\begin{frame}
\frametitle{Geometric likelihood}
\begin{itemize}
\item As mentioned in LHC we have different production sources of $\Ptau$'s.
\item Each source has different detector response signature.
\item To maximise our performance we trained classifiers for each of the $\Ptau$ sources using:
\begin{itemize}
\item Kinematic properties of $\Ptau$ candidate.
\item Geometric properties of $\Ptau$ candidate, like pointing angle, DOCA, Vertex $\chi^2$, flight distance.
\item Isolations, for vertex and individual tracks.
\end{itemize}
\item After training the individual classifiers one that combines all this information in a single classifier on mixed sample of $\Ptau$'s.
\item This technique is known as Blending or Ensemble learning.
\item Using this approach we gain $6\%$ sensitivity!
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Performance of Blend classifier}
\begin{itemize}
\item Classifier prefers $\Ptau$'s from prompt $\PDs$, the dominant channel.
\end{itemize}
\begin{columns}
\begin{column}{.49\textwidth}
\begin{exampleblock}{MC response for different\newline $\color{white} \tau$ production channels}
\includegraphics[width=.98\textwidth]{./mixing.pdf}
\end{exampleblock}
\end{column}
\begin{column}{.49\textwidth}
\begin{exampleblock}{Response for $\color{white} D_s \rightarrow \phi\pi$\newline data and MC}
\includegraphics[width=.98\textwidth]{./dataMC.pdf}
\end{exampleblock}
\end{column}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Calibration}
\begin{itemize}
\item Assume all differences between $\Ptau\to\Pmu\Pmu\Pmu$ and $\PDs\to\Pphi\Ppi$ come from kinematics (mass, resonance, decay time), which is correct in MC.
\item Get correction $\PDs\leadsto\Ptau$ from MC.
\item Apply corrections to $\PDs\to\Pphi\Ppi$ on data.
\end{itemize}
\begin{columns}
\begin{column}{.45\textwidth}
\includegraphics[width=.95\textwidth]{m3body_2012.pdf}
\end{column}
\begin{column}{.45\textwidth}
\begin{itemize}
\item $\PDs\to\Pphi\Ppi$ well modelled in MC.
% \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$
\end{itemize}
\end{column}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
% PID
\begin{frame}
\frametitle{PID}
\begin{itemize}
\item Classifier trained on inclusive MC sample.
\item Using information from: RICH, Calorimeters, Muon system and tracking.
\item Correct for the MC efficiency using control channel: $\PDs \to \Pphi(\Pmu\Pmu) \Ppi$ and $\PB \to \PJpsi(\Pmu\Pmu) \PK$
\end{itemize}
\begin{columns}
\begin{column}{.45\textwidth}
\includegraphics[width=.95\textwidth]{mPID_2012.pdf}
\end{column}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}
\frametitle{Binning optimisation}
\begin{itemize}
\item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane.
\item In 2D we group the events in groups(bins)
\item Bins are optimised using $CL_s$ method.
\item The lowest bins are rejected, because they do not contribute to the limit sensitivity.
\item In rest of the bins a fit to mass side-bands is performed in order to estimate number of expected background in signal window.
\end{itemize}
\begin{columns}
\column{2.5in}
\center{2011}\\
\includegraphics[width=.85\textwidth]{2D_2011.pdf}
\column{2.5in}
\center{2012}\\
\includegraphics[width=.85\textwidth]{2D_2012.pdf}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Mass shape}
\begin{itemize}
\item Double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian).
\item Fix fraction to ease calibration.
\item Correct mass by MC:\newline
$\sigma_{data}^{\Ptau} = \frac{\sigma_{MC}^{\Ptau}}{\sigma_{MC}^{\PDs}}\times\sigma_{data}^{\PDs}$
\end{itemize}
\includegraphics[width=.44\textwidth]{./Ds_data_2011.pdf}
\includegraphics[width=.44\textwidth]{./Ds_data_2012.pdf}
{\footnotesize{
\begin{tabular}{|c|c|c|}
\hline
Calibrated $\Ptau$ Mass shape & 7~TeV & 8~TeV\\
\hline
Mean ($\MeV$) & $1779.1 \pm 0.1$ & $1779.0 \pm 0.1$\\
\hline
$\sigma_1$ ($\MeV$) & $7.7 \pm 0.1$ & $7.6 \pm 0.1$\\
\hline
$\sigma_2$ ($\MeV$) & $12.0 \pm 0.8$ & $11.5 \pm 0.5$\\
\hline
\end{tabular}
}
}
\end{frame}
\section{Normalisation}
\begin{frame}
\frametitle{Relative normalisation}
$\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}$
\begin{itemize}
\item where $\varepsilon$ stands for trigger, reconstruction, selection efficiency.
\item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$.
\item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$
\newline i.e.\ $(83\pm3)\,\%$ for 2012.
\end{itemize}
\includegraphics[width=.47\textwidth]{./Ds_data_2011.pdf}
\includegraphics[width=.47\textwidth]{./Ds_data_2012.pdf}
\end{frame}
\section{Backgrounds}
\begin{frame}
\frametitle{Misidentification}
\begin{columns}
\column{3in}
\begin{itemize}
\item Most dominant: $\PDplus\to\PK\Ppi\Ppi$.
\item Also seen $\PDplus\to\Ppi\Ppi\Ppi$ and $\PDs\to\Ppi\Ppi\Ppi$.
\item All contained in the lowest $\mathcal{M}_{PID}$ bin.
% \item Experience from last round: cut away \\low ProbNNmu range
% \item Check remaining data under \\$\PK\Ppi\Ppi$ hypothesis for $\PDplus$ peak
% \item[$\Rightarrow$] misid safely contained in ``trash'' bin
\end{itemize}
\column{2in}
\includegraphics[width=.95\textwidth]{./WMH.pdf}
\end{columns}
\includegraphics[width=.45\textwidth]{./trash.pdf}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}{~}
\includegraphics[width=.45\textwidth]{./mPID_2012.pdf}
\end{frame}
\begin{frame}
\frametitle{Dangerous backgrounds}
\begin{columns}
\column{3in}
\begin{itemize}
\item $\Pphi\to\Pmu\Pmu + X$: narrow veto on dimuon mass.
\item $\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$: not so easy:
\begin{itemize}
\item Model it
\item \underline{Remove it} with dimuon mass cut:
\begin{itemize}
\item Fits better understood.
\item Sensitivity unchanged when removing veto.
\item Smaller uncertainty on expected background.
\end{itemize}
\end{itemize}
\end{itemize}
\column{2in}
\includegraphics[width=.95\textwidth]{./etaMass.pdf}\\
\includegraphics[width=.95\textwidth]{./etaDalitz.pdf}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Remaining backgrounds}
\begin{itemize}
\item Fit exponential to invariant mass spectrum in each likelihood bin.
\item Don't use blinded region ( $\pm \unit{30}{\MeV}$ ).
\item[$\rightarrow$] Compatible results blinding only $\pm \unit{20}{\MeV}$\footnote{partially used in classifier development}
\end{itemize}
{\begin{center}
Example of most sensitive regions in 2011 and 2012
\includegraphics[width=0.9\textwidth]{./fits.png}
\end{center}}
\end{frame}
\section{Model dependence}
\begin{frame}
\frametitle{Model dependence}
\begin{itemize}
\item $\Peta$ veto $\Rightarrow$ our limit not constraining to New Physics with small $m_{\APmuon\Pmuon}$.
\item Model description in \href{http://arxiv.org/abs/0707.0988}{\color{blue}\texttt{arXiv:0707.0988}} by S.Turczyk.
\item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms.
\end{itemize}
\only<2->{
\begin{itemize}
\item With radiative distribution limit gets worse by a factor of $1.5$ (dominantly from the $\Peta$ veto).
\item The other four Dalitz distributions behave nicely (within $7\,\%$).
\end{itemize}
\begin{center}
\includegraphics[width=.5\textwidth]{./sigDalitz.pdf}
\end{center}
}
\only<1>{
\begin{columns}
\column{0.33\textwidth}
\includegraphics[width=.95\textwidth]{./gammallll2.pdf}\\
\includegraphics[width=.95\textwidth]{./gammarad-llll2.pdf}
\column{0.33\textwidth}
\includegraphics[width=.95\textwidth]{./gammallrr2.pdf}\\
\includegraphics[width=.95\textwidth]{./gammarad-llrr2.pdf}
\column{0.33\textwidth}
\includegraphics[width=.95\textwidth]{./gammarad2.pdf}\\
% \begin{itemize}
% \item Same models as in Z.Was \href{https://indico.cern.ch/event/300387/session/7/contribution/33}{\color{blue}talk}
% \end{itemize}
{~}\\ {~}\\ {~}\\ {~}\\ {~}\\
\end{columns}
}
\end{frame}
% \begin{frame}
% \frametitle{Conclusion}
% \begin{columns}
% \begin{column}{.55\textwidth}
% \begin{itemize}
% \item finally all pieces put together
% \item model (in)dependence of $\Peta$ veto investigated
% \item expected sensitivity computed\newline $5.6\times 10^{-8}$
% \end{itemize}
% \end{column}
% \begin{column}{.45\textwidth}
% \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg}
% \end{column}
% \end{columns}
% \end{frame}
\section{Results}
\begin{frame}
\frametitle{Results}
\begin{center}
\includegraphics[width=0.7\textwidth]{banana_line.pdf}
\end{center}
\begin{columns}
\column{0.2in}{~}
\column{2in}
Limits(PHSP):\\
Observed(Expected)\\
$\color{red}4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\
$\color{pink}5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\
\column{3in}
\includegraphics[width=0.5\textwidth]{model.png}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{"The Rule of Three"}
\begin{columns}
% \column{2.5in}
\begin{column}{2.1in}
\begin{alertblock}{ $\Ptau \to \Pmu \Pmu \Pmu$ limits ($ \color{white} 90\,\%$ CL)}
\begin{description}
\item[BaBar(FC)] $3.3\times 10^{-8}$
\item[Belle(FC)] $2.1\times 10^{-8}$
\item[LHCb(CLs)] $4.6\times 10^{-8}$
\item[HFAG(CLs)] $1.2 \times 10^{-8}$
\end{description}
\end{alertblock}
\end{column}
\begin{column}{2.5in}
\includegraphics[width=1\textwidth]{zom.png}\\
{~}From A.Lusiani \href{https://indico.cern.ch/event/300387/session/6/contribution/12}{\color{blue}talk}
\end{column}
\end{columns}
{~}\\
To conclude:
\begin{itemize}
\item LHCb updated $\Ptau \to \Pmu \Pmu \Pmu$ with full data set.
\item We are getting close to B-factories.
\item Thanks to 3 experiments we have a world limit: $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL.
\end{itemize}
\end{frame}
\end{document}
mchrzasz