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- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
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-
-
- \usetheme{Sybila}
- \title[Search for Charged Lepton Flavour Violation at LHCb experiment]{Search for Charged Lepton Flavour Violation at LHCb experiment}
- \subtitle{Doctoral disertation}
- \author[Marcin Chrz\k{a}szcz]{Marcin Chrz\k{a}szcz \\ Supervisor: prof. dr hab. Tadeusz Lesiak \\ Auxiliary supervisor: dr hab. Alberto Lusiani}
-
- \institute[UZH, IFJ]{
- Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland}
-
-
- \date{\today}
- \begin{document}
-
-
- % --------------------------- SLIDE --------------------------------------------
- \frame[plain]{\titlepage}
- \author{Marcin Chrz\k{a}szcz}
- % ------------------------------------------------------------------------------
- % --------------------------- SLIDE --------------------------------------------
-
- \institute{~(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}
-
-
- \iffalse
-
- \begin{frame}
- \frametitle{Errata to thesis}
- \begin{itemize}
- \item Since submision, the HFAG report has been published, so refence:
- \end{itemize}
- [53] HFAG Collaboration, M.Chrz\k{a}szcz et. al. Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2014, arXiv:1412.7515.
- \end{frame}
-
-
- \fi
-
- \section{Lepton Flavour Violation phenomenon}
- \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}
- %%%%%%%%%%%%%%%%%
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \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 Superb particle identification (PID).
- \end{itemize}
-
-
-
- \end{footnotesize}
- \end{columns}
-
- \end{frame}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \section{Selection}
- \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.
- \item Event selection:
- \begin{itemize}
- \item Preselection of three tracks that combine to give a mass close to $m_{\tau}$, with desplaised vertex.
- \item Selection based on three classifiers:
- \begin{itemize}
- \item Geometry and topology ($\mathcal{M}_{3body}$)
- \item PID ($\mathcal{M}_{PID}$)
- \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 $\PD \to \PK \Ppi \Ppi$.
- \item Evaluation of the upper limit on $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)$ using $CL_s$.
- \end{enumerate}
-
-
- \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{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{Triggers at LHCb}
- \begin{footnotesize}
-
- \begin{itemize}
- \item LHCb uses complex trigger, $\mathcal{O}(100)$ trigger lines. %\footnote{\href{http://arxiv.org/abs/1211.3055}{\color{blue}arXiv:1211.3055}}, $\mathcal{O}(100)$ trigger lines.
- \item Lines change with data taking.
- \item Optimized choice of triggers based on $\dfrac{s}{\sqrt{b}}$ FOM,
- \end{itemize}
- \end{footnotesize}
- \begin{tiny}
- \begin{columns}
- \column{0.66\textwidth}
- \begin{equation}
- \label{eq:efftrig}
- \varepsilon(\beta)^\prime_{\text{evt},\text{line}} = \frac{N(\tau~\text{ MC(BKG) events triggered
- line, but not by any better line})}{N(\tau\text{ MC(BKG) events triggered by any line})}, \nonumber
- \end{equation}
- \begin{small}
- \begin{itemize}
- \item Evaluated different triggers used in 2012 data taking.
- \item Found negligible differences in trigger efficiencies.
- \end{itemize}
- \end{small}
- \column{0.32\textwidth}
- \begin{equation}
- \text{CTFM}=\frac{\sqrt{\sum\limits_\text{trigger lines} \beta^\prime_{\text{evt},\text{line}}}}{\sum\limits_\text{trigger lines} \varepsilon^\prime_{\text{evt},\text{line}}}\nonumber
- \end{equation}
-
- \end{columns}
- \end{tiny}
- \begin{footnotesize}
-
-
- \end{footnotesize}
- \begin{tiny}
- \begin{tabular}{|l|c|c|c|}
- \hline
- name & $\varepsilon^\prime$ & $\beta^\prime$ & CTFM \\\hline
- % here
- Hlt2TriMuonTauDecision & 0.880708 & 0.736182 & 0.974228\\
- Hlt2DiMuonDetachedDecision & 0.0669841 & 0.173396 & 1.00636\\
- Hlt2CharmSemilep3bodyD2KMuMuDecision & 0.0206816 & 0.0182935 & 0.99472\\
- Hlt2CharmHadD2HHHDecision & 0.00554351 & 0.00666405 & 0.992604\\
- Hlt2CharmSemilep3bodyD2KMuMuSSDecision & 0.00195444 & 0.00470404 & 0.993106\\
- Hlt2CharmSemilep3bodyD2PiMuMuDecision & 0.00206105 & 0.00679472 & 0.994591\\
- Hlt2TopoMu3BodyBBDTDecision & 0.00394442 & 0.0121521 & 0.996937\\
- \hline
- \end{tabular}
- \end{tiny}
-
-
-
- \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{Particle Identification (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{2.2in}
- \center{2011}\\
- \includegraphics[width=.99\textwidth]{2D_2011.pdf}
- \column{2.2in}
- \center{2012}\\
- \includegraphics[width=.99\textwidth]{2D_2012.pdf}
- \column{0.5in}
- {~}
-
- \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}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
- \section{LFV limit combination}
-
-
- \begin{frame}\frametitle{Combination of LFV UL 1/2}
- \begin{columns}
-
- \column{1.8in}
- \begin{itemize}
-
- \item Searches for LFV in $\Ptau$ sector is a domain of B factories.
- \item Over last years both BaBar and Belle set very strong limits on branching fractions of several rare $\tau$ decays.
-
- \end{itemize}
-
-
- \column{3.2in}
- \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001.png}
-
-
-
- \end{columns}
- \begin{itemize}
- \item Since thouse limits are used to constraint NP models, their "official" combination is of paramount importance.
- \item Various methods of limit computation used in Belle and BaBar's studies.
- \item The HFAQ group recomputed consistently all estimates using the $CL_s$ method and the the same approach was involved in the average evaluation.
- \end{itemize}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
-
- \begin{frame}\frametitle{Combination of LFV UL 2/2}
- \begin{itemize}
- \item For each measurement take integrated luminosity ($\mathcal{L}$), cross section ($\sigma_{\tau\tau}$), efficiencies ($\epsilon$), background expected($b$) and all systematics.
- \item Calculate number of signal: $s = \mathcal{L} \sigma_{\tau\tau} \epsilon^{tot} \mathcal{B}(\Ptau \to LFV)$.
- \item Scan the $CL_s$ wrt. $\mathcal{B}(\Ptau \to LFV)$:
- \end{itemize}
- \begin{columns}
- \column{0.15in}
- {~}
- \column{2in}
- \begin{small}
- \begin{align}
- 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{align}
- \end{small}
- \column{2.7in}
- \includegraphics[width=0.95\textwidth]{TauLFV_UL_2014001_averaged.png}
-
-
- \end{columns}
- \end{frame}
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- \begin{frame}
- \frametitle{"The Rule of Three"}
- \begin{columns}
- % \column{2.5in}
- \begin{column}{1.9in}
- \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}{2.85in}
- \includegraphics[width=1\textwidth]{TauLFV_UL_2014001_averaged_zoom.png}\\
-
- \end{column}
-
- \end{columns}
- {~}\\
-
-
- To conclude:
- \begin{columns}
- \column{3in}
- \begin{small}
- \begin{itemize}
- % \item LHCb result for $\Ptau \to \Pmu \Pmu \Pmu$ 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.
- \item LHCb is reaching B-factories limits.
- \item Many new techniques developed to perform this analysis.
- \item Combination of UL within HFAG gave the best sensitivity for $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)< 1.2 \times 10^{-8}$ at 90\% CL.
-
- \end{itemize}
- \end{small}
- \column{2in}
- \includegraphics[width=0.93\textwidth]{banana_tau23mu_hfag.pdf}\\
-
-
- \end{columns}
-
- \end{frame}
-
- \pagenumbering{gobble}
- \begin{frame}\frametitle{Backup}
-
- \includegraphics[width=0.93\textwidth]{ngbbs4f7918ec8ffb8.jpg}\\
-
-
- \end{frame}
-
-
-
-
-
- \begin{frame}\frametitle{Prof. J.Ciborowski comments}
- \begin{enumerate}
- \item Podrozdział (4.10) ten jest de facto zapowiedzią większej pracy. Szkoda, że materiał tu przedstawiony
- potraktowany został bardzo skrótowo, co wymusiło na mnie konieczność kilkakrotnego przeczytania tego podrozdziału i utrudniło docenienie wyniku
- otrzymanego przez autora w konfrontacji z przewidywaniami teoretycznymi.
- \end{enumerate}
- \begin{itemize}
- \item The theory part of this was presented in detail in 2.3.4. This chapter is just a showing how to reweight the distributions to a given NP model, thats why I tried to keep it short, but I agree I over did it.
- \end{itemize}
-
-
- \end{frame}
-
-
-
- \begin{frame}\frametitle{Prof. J.Ciborowski comments}
- \begin{enumerate}
- \item Jedyne
- rzucające się w oczy uchybienie redakcyjne to pomyłki w numerach
- rozdziałów, których zawartość wymieniona jest pod koniec Wstępu.
-
- \end{enumerate}
- \begin{itemize}
- \item Mea Cupla. Completly missed that.
- \end{itemize}
-
-
- \end{frame}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5555
-
-
-
- \end{document}