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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[$\tau \to \mu\mu\mu$ in LHCb]{$\tau \to \mu\mu\mu$ in LHCb}
\date{25 September 2014}
\begin{document}
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\begin{center}
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\begin{columns}
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\flushright\fontspec{Trebuchet MS}\bfseries \Huge {$\tau \to \mu\mu\mu$ in LHCb}
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\quad
\vspace{3em}
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\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
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\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}{Kaggle Seminar, San Francisco\\August 21, 2015}
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\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 there is a nother $\Pnu$.
\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 LNV (Majorana neutrinos)
\item LNV searched in s-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 searches for $\color{white} \tau \to \mu \mu \mu$}
\begin{columns}
\begin{column}{.62\textwidth}
\includegraphics[width=.95\textwidth]{feymn.png}
{{
\begin{itemize}
\item Charged Lepton Flavour Violation process.
\item The Standard Model contribution: penguin diagram 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] $2.1\times 10^{-8}$
\end{description}
\end{alertblock}
\begin{alertblock}{Predictions}
\begin{description}
\item[SM] $ O(10^{-40})$
\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}
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\begin{frame}
\frametitle{$\tau$ production}
\begin{itemize}
\item $\Ptau$'s in LHCb come from five main sources:
\end{itemize}
\begin{center}
\begin{footnotesize}
\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{footnotesize}
\begin{itemize}
\item Pythia produces them in wrong propotions
\item Channels were produced seperatly and added in the given proporitons.
\end{itemize}
\end{center}
\begin{columns}
\column{0.05\textwidth}
{~}
\column{0.9\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, \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{Signal and background discrimination}
\begin{itemize}
\item Two multivariate classifiers, $\mathcal{M}_{3body}$ and $\mathcal{M_{PID}}$.
\end{itemize}
\begin{columns}
\column{3in}
\begin{itemize}
\item $\mathcal{M}_{3body}$ trained using vertex and track fit quality, vertex displacement, vertex pointing, vertex isolation and $\Ptau$ $p_T$.
\item Used Blending Technique (see the next slide).
\end{itemize}
\column{2in}
\includegraphics[width=.98\textwidth]{ver.png}
\end{columns}
\begin{columns}
\column{0.1in}
{~}
\column{2in}
% \includegraphics[width=.95\textwidth]{m3body_2012.pdf}
\includegraphics[angle=-90,width=.98\textwidth]{images/mixing.pdf}
\column{3in}
\begin{itemize}
\item Trained on signal and background MC.
\item Calibrated on $\PDs \to \Pphi(\mu\mu) \Ppi$ sample.
\end{itemize}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Blending technique}
\begin{columns}
\column{3.2in}
\includegraphics[width=.99\textwidth]{diagram.png}
\column{1.8in}
\begin{itemize}
\item Each of the $\Ptau$ lepton production channel have a different signature in terms of kinematic distributions.
\item Signal blending technique improved the discriminating power by $6~\%$
\end{itemize}
\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 $\PDs \Longrightarrow \Ptau$ from MC.
\item Apply corrections to $\PDs\to\Pphi\Ppi$ on data.
\item Publication in preparation.
\end{itemize}
\begin{columns}
\begin{column}{.45\textwidth}
\includegraphics[angle=-90,width=.95\textwidth]{images/m3body_2012.pdf}
\end{column}
\begin{column}{.45\textwidth}
\begin{itemize}
\item $\PDs\to\Pphi\Ppi$ decay well modelled in MC.\\
\includegraphics[angle=-90,width=.9\textwidth]{images/dataMC.pdf}
% \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$
\end{itemize}
\end{column}
\end{columns}
\end{frame}
\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}
\begin{frame} \frametitle{Remaining backgrounds}
\begin{itemize}
\item Fit exponential to invariant mass spectrum in each likelihood bin.
\item Don't use the $\pm 30~\MeV$ region.
% \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}
\begin{frame}
\frametitle{Results}
\begin{center}
\includegraphics[angle=-90,width=0.7\textwidth]{images/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=0.45\textwidth]{model.png}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Why are we not putting the mass in the classifier?}
$\Rrightarrow$ Why don't we put mass in the classifier?\\
$\rightrightarrows$ Many reasons:\\
\begin{itemize}
\item Our normalization channel is in different mass range!
\item Mass resolution is wrongly modelled in MC.
\item Easily to interpret:
\end{itemize}
\begin{columns}
\column{0.05\textwidth}
\column{0.45\textwidth}
\includegraphics[width=0.95\textwidth]{mass2.png}
\column{0.45\textwidth}
\includegraphics[angle=-90, width=0.95\textwidth]{{images/10500_11000_y_bin_2_4.5}.pdf}
\column{0.05\textwidth}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Data agreement check, why do we bother?}
$\Rrightarrow$ It all boils down to our equation:
$\boxed{\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}}$\\{~}\\
There are 3 variables that we need to terminate: $\varepsilon_\text{sig}$, $\varepsilon_\text{norm}$ and $N_\text{norm}$.
\begin{itemize}
\item $\varepsilon_\text{norm}$; determine from data, by a cut and count method.
\item $N_\text{norm}$; determined from data by a simple fit.
\item $\varepsilon_\text{sig}$; calibrated on data:
\end{itemize}
\begin{align*}
\varepsilon_\text{sig}=\varepsilon_\text{sig}^\text{MC} \frac{\varepsilon_\text{norm}^\text{DATA}}{\varepsilon_\text{norm}^\text{MC}}
\end{align*}
The hack that is used here is: $\varepsilon_\text{sig}$ is ok, but $N_\text{norm}$ is smaller, so alpha is bigger $\Rightarrow$ worse sensitivity.
\end{frame}
\begin{frame}\frametitle{Wrap up}
\begin{enumerate}
\item Physics has a different application of ML than computer science.
\item There are physics consequance of what you use!
\item Blindly taking all varaibles is the bad solution.
\end{enumerate}
\end{frame}
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mchrzasz