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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 \href{https://indico.cern.ch/event/300387/session/17/contribution/74}{J. Harrison 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, ``geometry/topology''.
\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 complicated trigger\footnote{\href{http://arxiv.org/abs/1211.3055}{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 LHCb 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
\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{block}{validation}
\begin{itemize}
\item done for 2011 analysis, treating smeared MC as data
\end{itemize}
\end{block}
\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}
\begin{frame}
\frametitle{PID calibration }
\begin{exampleblock}{Phenomenological treatment}
\begin{itemize}
\item correlations are small in $\PDs\to\Pphi\Ppi$ data and MC:
\newline $\varepsilon(\text{cut on one muon})^2 = \varepsilon(\text{cut on two muons})$
\item[$\Rightarrow$] use $c^3=(\varepsilon(\text{cut and fit})/\varepsilon(\text{PIDCalib}))^3$ as correction to PIDCalib for $\Ptau\to\Pmu\Pmu\Pmu$
\item assign error of $0.02$ for $c$.
\end{itemize}
\end{exampleblock}
\begin{itemize}
\item Many cross-checks done.
\item Everything works fine.
\end{itemize}
\begin{columns}
\begin{column}{.45\textwidth}
\includegraphics[width=.95\textwidth]{mPID_2012.pdf}
\end{column}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Binning optimisation}
\begin{itemize}
\item How to optimise the binning in two classifiers?
\item $\unit{1}{\reciprocal\femtobarn}$ CONF note: two one-dimensional optimisations as in $\PBs\to\Pmu\Pmu$.
\item $\unit{1}{\reciprocal\femtobarn}$ PAPER: iterative loop of one-dimensional optimisations\newline optimising one classifier on the sensitive range of the other classifier.
\item Now: optimise two-dimensions (optimise bin boundaries in both dimensions simultaneously).
\item Unchanged: don't use lowest likelihood bins\newline(reflection backgrounds, no sensitivity gain).
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Impact of new binning optimisation}
\begin{itemize}
\item Removal of tiny bins which contribute negligible sensitivity.
\item Colour: limit obtained, using only this particular bin.
\item Number: rank of that bin (1=best sensitivity bin).
\end{itemize}
\begin{columns}
\begin{column}{.8\textwidth}
\begin{center}
Bin sensitivity
(2011 data)
\end{center}
\includegraphics[width=.95\textwidth]{./rank.pdf}
\end{column}
\begin{column}{.2\textwidth}
{~}
\end{column}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Mass shape}
\begin{itemize}
\item Double-Gaussian with fixed fraction ($70\,\%$ inner Gaussian).
\item Fix fraction to ease calibration.
\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,
\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}
\begin{frame}[allowframebreaks]
\frametitle{Normalisation in numbers}
{\footnotesize{
$\begin{array}{c|c|c}
& \rm{7~TeV} & \rm{8~TeV}\\
\hline
\rm{\epsilon\mathstrut_{sig}}^{GEN} (\%) & 8.989 \pm 0.40 & 9.21 \pm 0.35\\
\hline
\rm{\epsilon_{cal}}^{GEN} (\%) & 11.19 \pm 0.34 & 11.53 \pm 0.32\\
\hline
\rm{\epsilon_{sig}}^{REC,isMuon,SEL} (\%) & 9.927 \pm 0.028 & 9.261 \pm 0.023 \\
\hline
\rm{\epsilon_{cal}}^{REC,isMuon,SEL} (\%) & 7.187 \pm 0.022 & 6.690 \pm 0.022 \\
\hline
\frac{\rm{c_{cal}}^{track}}{\rm{c_{sig}}^{track}} & 0.997 \pm 0.009 \pm 0.026 & 0.996 \pm 0.009 \pm 0.026 \\
\hline
\frac{\rm{c_{cal}}^{\mu ID}}{\rm{c_{sig}}^{\mu ID}} & 0.9731 \pm 0.0031 \pm 0.0264 & 1.0071 \pm 0.0022 \pm 0.0204 \\
\hline
\rm{c}^{\phi} & \multicolumn{2}{c}{0.98 \pm 0.01} \\
\hline
\rm{c}^{\tau} & 1.032 \pm 0.006 & 1.026 \pm 0.006\\
\hline
\rm{c}^{trash} & 1.89 \pm 0.12 & 1.96 \pm 0.12\\
\hline
\rm{\epsilon\mathstrut_{sig}}^{TRIG} (\%) & 35.52 \pm 0.14 \pm 0.14 & 39.3 \pm 1.7 \pm 2.0 \\
\hline
\rm{\epsilon\mathstrut_{cal}}^{TRIG} (\%) & 23.42 \pm 0.14 \pm 0.09 & 20.62 \pm 0.76 \pm 1.07 \\
\end{array}$
}}
\framebreak
{\footnotesize{
$\begin{array}{c|c|c}
& \rm{7~TeV} & \rm{8~TeV}\\
\hline
\mathcal{B}(\PDs \to \Pphi \Ppi) & \multicolumn{2}{c}{(1.317 \pm 0.099) \times 10^{-5}}\\
\hline
f^{\tau}_{D_{s}} & 0.78 \pm 0.04 & 0.80 \pm 0.03 \\
\hline
\mathcal{B} (\PDs \to \Ptau \Pnut) & \multicolumn{2}{c}{0.0561 \pm 0.0024}\\
\hline
\rm{\epsilon\mathstrut_{cal}}^{REC\&SEL}/
\rm{\epsilon\mathstrut_{sig}}^{REC\&SEL}
& 0.898 \pm 0.060 & 0.912 \pm 0.054 \\
\hline
\rm{\epsilon\mathstrut_{cal}}^{TRIG}/
\rm{\epsilon\mathstrut_{sig}}^{TRIG}
& 0.6593 \pm 0.0058 & 0.525 \pm 0.040\\
\hline
N_{cal} & 28,207 \pm 440 & 52,131 \pm 695\\
\hline & \\[-0.8em]\hline
\alpha & (3.81 \pm 0.46) \times 10^{-9} & (1.72 \pm 0.23) \times 10^{-9}\\
\alpha^{trash} & (7.20 \pm 0.98) \times 10^{-9} & (3.37 \pm 0.50) \times 10^{-9}\\
\end{array}$
}}
\end{frame}
\section{Backgrounds}
\begin{frame}
\frametitle{Misidentification 1}
\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 Looked in all mass hypothesis combinations.
% \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]{./Dp2Kpipi_all_2012_senseBins.pdf}
\includegraphics[width=.45\textwidth]{./FittoD23pi_2012.pdf}
\end{frame}
\begin{frame}
\frametitle{Misidentification 2}
\begin{itemize}
\item Many tests were performed to be sure we are safe from $\PD_x \to 3h$.
\item Tested both on MC and data.
\item Referees also suggest looking into semileptonic decays.
\item Our background is safely contained in ''trash''\footnote{\begin{tiny} Lowest $ProbNNmu$ and $M_{blend}$ bins, not taken for limit calculation. \end{tiny}} bins.
\end{itemize}
\includegraphics[width=.7\textwidth]{./c_2dHisto_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 Modelled in CONF note.
\item Optimised veto in PAPER.
\item Both versions in the ANA note.
\end{itemize}
\item Baseline: veto $m_{\APmuon\Pmuon} < \unit{450}{\MeV}$:
\begin{itemize}
\item Fits better understood.
\item Sensitivity unchanged when removing veto.
\item Smaller uncertainty on expected background.
\end{itemize}
\end{itemize}
\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{Expected limit}
\begin{frame}
\frametitle{Expected limit}
\begin{itemize}
\item Consider nuisance parameters from background fit, signal pdf calibration, normalisation.
\item Nuisance parameters due to $\Ptau$ production, normalization.
\item Limit for combined 2011+2012 analysis.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Sensitivity}
$\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu)<5.0 \times 10^{-8}$ at 90\% CL
\includegraphics[width=.8\textwidth]{limit_blind.png}
\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 \texttt{arXiv:0707.0988}.
\item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms.
\end{itemize}
\only<2->{
\begin{itemize}
\item With radiative distribution limit gets worse by a factor of $1.5$ (dominantly from the $\Peta$ veto).
\item The other four Dalitz distributions behave nicely (within $7\,\%$).
\end{itemize}
}
\only<1>{
\includegraphics[width=.331\textwidth]{./gammallll.pdf}
\includegraphics[width=.331\textwidth]{./gammallrr.pdf}
\includegraphics[width=.331\textwidth]{./gammarad.pdf}
\includegraphics[width=.331\textwidth]{./gammarad-llll.pdf}
\includegraphics[width=.331\textwidth]{./gammarad-llrr.pdf}
}
\end{frame}
% \begin{frame}
% \frametitle{Conclusion}
% \begin{columns}
% \begin{column}{.55\textwidth}
% \begin{itemize}
% \item finally all pieces put together
% \item model (in)dependence of $\Peta$ veto investigated
% \item expected sensitivity computed\newline $5.6\times 10^{-8}$
% \end{itemize}
% \end{column}
% \begin{column}{.45\textwidth}
% \includegraphics[width=\textwidth]{party-music-hd-wallpaper-1920x1200-3850.jpg}
% \end{column}
% \end{columns}
% \end{frame}
\section{Unblinded results}
\begin{frame}
\frametitle{Unblinding 1}
\begin{columns}
\column{1in}{~}
\column{3in}
''
THERE came a day at summer’s full \\
Entirely for us \\
I thought that such were for the saints, \\
Where revelations be. ''\footnote{E.Dickinson} \\
\column{1in}{~}
\end{columns}
{~}\\
{~}\\
\begin{Large}
On Monday $4^{th}$ of August we were given the permission to unblind.
\end{Large}
\end{frame}
\begin{frame}
\frametitle{Unblinding 2}
\begin{itemize}
\item Unfortunately no big ''revelations'' were there.
\item 2011 numbers:
\end{itemize}
\includegraphics[width=1.\textwidth]{2011.png}
\end{frame}
\begin{frame}
\frametitle{Unblinding 3}
\begin{itemize}
\item Unfortunately no big ''revelations'' were either in 2012 data:
\end{itemize}
\includegraphics[width=1.1\textwidth]{2012.png}
\end{frame}
\begin{frame}
\frametitle{Unblinding 4}
\begin{center}
\includegraphics[width=0.7\textwidth]{banana_line.pdf}
\end{center}
\begin{columns}
\column{0.2in}{~}
\column{2in}
Limits(PHSP):\\
Observed(Expected)\\
$4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\
$5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\
\column{3in}
\includegraphics[width=0.5\textwidth]{model.png}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Conclusions}
\begin{columns}
\column{2.5in}
\begin{itemize}
\item We didn't find NP (yet).
\item Limits set with full LHCb dataset.
\item We wait for the Run 2 dataset!
\end{itemize}
\column{2.5in}
\includegraphics[width=1\textwidth]{TauLFV_UL_2013001.pdf}
\end{columns}
\begin{itemize}
\item We would like to thank our referees for very friendly,thorough and fruitful review.
\item With this presentation we ask collaboration for approval.
\end{itemize}
\end{frame}
\end{document}
mchrzasz