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\title[ $\color{white} \tau \to \mu \mu \mu$ approval presentation ]{$\color{white} \tau \to \mu \mu \mu$ approval presentation}
\author[Marcin Chrzaszcz]{
Johannes Albrecht\inst{1}, Marta Calvi\inst{2,3}, \underline{Marcin Chrzaszcz}\inst{4,5}, \\Laura Gavardi\inst{1}, Jon Harrison\inst{6}, Basem Khanji\inst{3},\\ George Lafferty\inst{6}, Tatiana Likhomanenko\inst{7}, Eduardo Rodrigues\inst{6}, \\Nicola Serra\inst{4}, Paul Seyfert\inst{7}\\
\textbf{Referees}:\\ Benoit Viaud (Chair) , Matteo Rama, Frederic Machefert (EB) }
\institute[UZH, IFJ]{\begin{tiny}
$ ^1$ Fakult\"at Physik, Technische Universit\"at Dortmund, Germany\\
$ ^2$ The University of Milano Bicocca, Milano, Italy\\
$ ^3$ INFN Milano Bicocca, Milano, Italy\\
$ ^4$ Physik-Institut der Universit\"{a}t Z\"{u}rich, Switzerland\\
$ ^5$ Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland\\
$ ^6$ The University of Manchester, UK\\
$ ^7$ Yandex, Moscow, Russia \\
$ ^8$ Physikalisches Institut Heidelberg, Germany\\
\end{tiny}
}
\date{\today}
\begin{document}
% --------------------------- SLIDE --------------------------------------------
\frame[plain]{\titlepage}
\author{Marcin Chrz\k{a}szcz}
% ------------------------------------------------------------------------------
% --------------------------- SLIDE --------------------------------------------
\institute{~(UZH, IFJ)}
% \begin{frame}\frametitle{Outline}
% \begin{enumerate}
% \item introduction\vspace{.5em}
% \item multivariate technique\vspace{.5em}
% \item normalisation\vspace{.5em}
% % \item backgrounds\vspace{.5em}
% \item expected sensitivity\vspace{.5em}
% \item model dependence\vspace{.5em} data from Reco14Stripping20(r1)
% \end{enumerate}
% Major news wrt.\ the $1~fb^{-1}$ analysis are highlighted in \textcolor{mygreen}{green}
% \end{frame}
\begin{frame}\frametitle{Outline}
\tableofcontents
\end{frame}
\begin{frame}
\frametitle{Yellow pages}
\begin{itemize}
\item TWiki: \href{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}{\url{https://twiki.cern.ch/twiki/bin/viewauth/LHCbPhysics/Tau_LFV_3fb}}.
\item ANA note: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/v8.pdf}{LHCb-ANA-2014-005}.
\item Paper draft: \href{https://twiki.cern.ch/twiki/pub/LHCbPhysics/Tau_LFV_3fb/paper_v1.pdf}{LHCb-PAPER-2014-X}.
\item Target journal: JHEP.
\item Conference: Tau 2014.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
\begin{frame}
\frametitle{Status of $\color{white} \tau \to \mu \mu \mu$}
\begin{columns}
\begin{column}{.62\textwidth}
\includegraphics[width=.95\textwidth]{feymn.png}
{{
\begin{itemize}
\item Charged Lepton Flavour Violation process.
\item Possible as penguin with neutrino oscillation.
\item SM prediction is beyond experimental reach~$O(10^{-40})$.
\end{itemize}
}}
\end{column}
\begin{column}{.45\textwidth}
\begin{alertblock}{current limits ($ \color{white} 90\,\%$ CL)}
\begin{description}
\item[BaBar] $3.3\times 10^{-8}$
\item[Belle] $2.1\times 10^{-8}$
\item[LHCb] $8.0\times 10^{-8}$
\end{description}
\end{alertblock}
\begin{alertblock}{BSM predictions}
\begin{description}
\item[var.\ SUSY] $10^{-10}$
\item[non universal $\PZprime$] $10^{-8}$
\item[mSUGRA+seesaw] $10^{-9}$
\item[and many more...]
\end{description}
\end{alertblock}
\end{column}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Strategy}
\begin{itemize}
\item Following same approach as other RD searches.
\item Loose stripping selection.
\item Multivariate classification in: mass, PID, ``geometry/topology''.
\item Binning optimisation.
\item Relative normalisation ($\PDs\to\Pphi(\Pmu\Pmu)\Ppi$).
\item Invariant mass fit for expected background in each likelihood bin: fit in $\left| m-m_{\Ptau} \right| >\unit{30}{\MeV}$.
\item ``middle sidebands'' for classifier evaluation and tests.($\unit{20}{\MeV}<\left| m-m_{\Ptau}\right| <\unit{30}{\MeV}$).
\item CLs for limit calculation.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{$\color{white} \tau$ {\scriptsize production\begin{footnotesize}
{\small •}
\end{footnotesize}}}
\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{Datasets}
\begin{itemize}
\item Data from Reco14Stripping20(r1).
\item Large MC samples:
\begin{itemize}
\item 24M Inclusive background events ($\Pbottom\APbottom$ and $\Pcharm\APcharm$).
\item 10M Exclusive background events ($\PDs\to\Peta(\Pmu\Pmu\Pphoton)\Pmu\Pnum$).
\item 2M Signal events (split over 5 production channels).
\item 12M $\PD \to \PK \Ppi \Ppi$ (missID studies).
\item 10M $\PDstar \to \PD(\PK \Pmu \Pnum) \Ppi$ (missID studies).
\end{itemize}
\item[$\Rightarrow$] Generator level cuts for improved use of computing resources.
\begin{itemize}
\item $\sim 14$ times more signal statistics after stripping.
\item $\sim 2$ times more background statistics.
\end{itemize}
\item Mix $\Ptau$ production on ntuple level instead of reweighting.
\newline$\Rightarrow$ Ease up ntuple usage (no forgotten weighting, no double weighting, \dots).
\end{itemize}
\end{frame}
\section{Selection}
\begin{frame}
\frametitle{Stripping and selection}
{\footnotesize{
\begin{tabular}{|c|cc|}
\hline
&$\Ptau\to\Pmu\Pmu\Pmu$&$\PDs\to\Pphi\Ppi$\\
\hline
$\mu^\pm$ , $ \pi^\pm$ &\multicolumn{2}{c|}{} \\
$p_T$ &\multicolumn{2}{c|}{$>300\MeV$} \\
Track $\chi^2$/ndf &\multicolumn{2}{c|}{$<3 $} \\
IP $\chi^2$/ndf &\multicolumn{2}{c|}{$>9 $} \\
track ghost probability &\multicolumn{2}{c|}{$<0.3 $} \\
\hline
$\mu$ pairs &\multicolumn{2}{c|}{} \\
$m_{\mu^+\mu^-} - m_{\phi}$ & $>20\MeV$ & $<20\MeV$\\
$m_{\mu^+\mu^-}$ & $> 450\MeV$ & - \\
$m_{\mu^+\mu^+}$ & $> 250\MeV$ & - \\
\hline
$\tau^\pm$ and \PDs &\multicolumn{2}{c|}{} \\
$\Delta m$ & $<400\MeV$ & $<50\MeV$\\
Vertex $\chi^2$ &\multicolumn{2}{c|}{$<15$} \\
IP $\chi^2$ &\multicolumn{2}{c|}{$<225 $} \\
$\cos\alpha$ &\multicolumn{2}{c|}{$>0.99$} \\
$c\tau$ (stripping) &\multicolumn{2}{c|}{$>\unit{100}{\mu m}$} \\
&\multicolumn{2}{c|}{no PV refitting}\\
decay time (offline) &\multicolumn{2}{c|}{$> -0.01$ ns \& $< 0.025$ ns}\\
&\multicolumn{2}{c|}{PV refitting}\\
\hline
\end{tabular}
}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Triggers}
{\footnotesize{
\begin{tabular}{l|c|c}
& signal & normalisation \\\hline\hline
L0$^1$ & \multicolumn{2}{c}{L0Muon TOS}\\\hline
Hlt1$^1$ & \multicolumn{2}{c}{Hlt1TrackMuon TOS}\\\hline
Hlt2 2011 & Hlt2CharmSemilepD2HMuMu TOS & Hlt2DiMuonDetached$^2$ TOS \\
& $||$ Hlt2TriMuonTau TOS & \\\hline
Hlt2 2012 & Hlt2TriMuonTau$^1$ TOS & Hlt2DiMuonDetached$^2$ TOS\\\hline
\end{tabular}
}
}
\only<1>{
\begin{block}{Triggers in 2012}
\begin{itemize}
\item Cuts changed through 2012.
\item[$\rightarrow$]emulated two different TCKs for 2012.
\item[$\rightarrow$] Found negligible differences in ratio of signal/normalisation channels.
\item Choice of triggers was optimised based on $\dfrac{s}{\sqrt{b}}$ FOM.
\end{itemize}
\end{block}}
% \only<2>{
% \begin{block}{$^2$ word on Hlt2DiMuonDetached}
% \begin{itemize}
% \item keep it simple here
% \item line unchanged in 2012
% \item[$\rightarrow$] choice keeps Hlt2 trigger efficiency stable
% \item $\PDs\to\Pphi\Ppi$ anyhow doesn't behave like $\Ptau\to\Pmu\Pmu\Pmu$ in the TriMuon trigger (requires misidentification)
% \end{itemize}
% \end{block}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Multivariate technique}
\begin{frame}
\frametitle{Geometric likelihood}
Much work has been put into improving our geometric and kinematic classifier:
\begin{itemize}
\item Classify the displaced 3-body decay properties of a signal candidate.
\item Revisit variable choice.
\item Revisit classification technique.
\item More toolkits tried: MatrixNet, NeuroBayes, TMVA.
\item Retune input variables\newline($\PBs\to\Pmu\Pmu$ isolation $\rightarrow$ BDT isolation: CERN-THESIS-2013-259).
\item Apply Blending technique.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Basic Setup - Step I}
\begin{itemize}
\item Train $1/3$ signal MC against $1/2$ background MC.
\item Input variables: \begin{itemize}
\item DOCA
\item Vertex $\chi^2$
\item $\tau$ decay time
\item $\tau$ IP$\chi^2$
\item min.\ $\mu$ IP$\chi^2$
\item $\Ptau$ pointing angle
\item $\tau$ $p_T$
\item max.\ track $\chi^2$
\item $\PBs\to\Pmu\Pmu$ track isolation
\item Cone isolation
\item BDT isolation
\end{itemize}
\item Using these variables, train several classifiers (''Base'') \\for each of the $\Ptau$ source.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Step II}
\begin{itemize}
\item Train using second $1/3$ signal MC against second $1/2$ background MC.
\item Introduce Blending technique.
\end{itemize}
\begin{exampleblock}{Blending technique}
\begin{itemize}
\item For each signal channel we train: one BDT, three Fisher classifier, four MLPs, one FDA, one LD classifier and MatrixNet classifier.
\item One final MatrixNet classifier using the 13 base variables and the base classifiers as input.
\end{itemize}
\end{exampleblock}
\begin{itemize}
\item All evaluation is done on $3rd$ $1/3$ signal sample and middle side-bands.
\item Splitting into independent samples makes the procedure insensitive to
overtraining.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Performance of Blend classifier}
\begin{itemize}
\item Classifier prefers $\Ptau$'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}
\begin{itemize}
\item We used ProbNNmu already in the previous round of the analysis.
\item Now use MC12TuneV2.
\item Two-fold reason:\begin{itemize}
\item Expect better performance than CombDLL variables.
\item ``one variable for everything'':\newline with CombDLL we needed both CombDLL($\mu-\pi$) and CombDLL($\mu-K$).
\end{itemize}
\end{itemize}
\begin{columns}
\end{columns}
\begin{itemize}
\item We tested if PIDCalib samples~($\PJpsi$) are suited for us.
\item $\PDs \to \Pphi \Ppi$ better representing $\tau \to 3\mu$ than $\PJpsi \to \mu \mu$.
\item Many thanks to Barbara Sciascia for help understanding the details: \href{https://indico.cern.ch/event/250103/contribution/3/material/slides/0.pdf}{LINK}
\end{itemize}
\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}
Marcin Chrząszcz