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- \definecolor{darkpastelgreen}{rgb}{0.01, 0.75, 0.24}
-
-
- \usetheme{Sybila}
- \title[Search for Charged Lepton Flavour Violation at LHCb experiment]{Search for Charged Lepton Flavour Violation at LHCb experiment}
- \author[Marcin Chrz\k{a}szcz]{Marcin Chrz\k{a}szcz }
-
- \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{enumerate}
- \item Lepton Flavour Violation (LFV) found in neutrino sector - the first phenomena outside the Standard Model.
- \item The search for charged lepton flavour violation (CLFV) commenced with muon discovery (1936) and its identification as a separate particle.
- \end{enumerate}
- \begin{columns}
- \column{3in}
- \begin{itemize}
- \item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$
- \item Unless there is another $\Pnu$.
- \end{itemize}
-
- \column{2in}
- {~}\includegraphics[width=0.98\textwidth]{rabi.png}
-
- \end{columns}
- \begin{footnotesize}
-
- \begin{enumerate}
- \setcounter{enumi}{2}
- \item The observation of CLFV would be a clear signature of New Physics (NP) - paramount importance for flavour physics and the enigma of generations.
- \item LFV vs LNV (Lepton Number Violation)
- \end{enumerate}\end{footnotesize}
- \begin{columns}
- \column{3.5in}
- \begin{footnotesize}
-
-
- \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 so-called neutrinoless double $\beta$ decays.
- \end{itemize}
- \end{footnotesize}
- \column{1.5in}
- \includegraphics[width=0.65\textwidth]{Double_beta_decay_feynman.png}
-
- \end{columns}
-
-
- % \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}{.55\textwidth}
-
- \includegraphics[width=.90\textwidth]{feymn.png}
-
- {{
- \begin{small}
- \begin{itemize}
- \item Charged Lepton Flavour Violation process.
- \item The Standard Model contribution: penguin diagram with neutrino oscillation.
- \item Negligible SM branching fraction.
- \item Large enhacement from NP models like: SUSY, Little Higgs, Fourth generation, etc.
-
- % \item SM prediction is beyond experimental reach~$O(10^{-40})$.
-
- \end{itemize}
- \end{small}
- }}
- \end{column}
- \begin{column}{.45\textwidth}
-
- \begin{alertblock}{Predictions}
- \begin{description}
- \item[SM] $ O(10^{-40})$
- \item[var.\ SUSY] $10^{-10}$
- \item[non universal $\color{red}{Z'}$] $10^{-8}$
- \item[mSUGRA+seesaw] $10^{-9}$
- \item[and many more...]
- \end{description}
- \end{alertblock}
-
- \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}
- \includegraphics[width=.63\textwidth]{SUSY.png}
-
- \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 in the region of $| m_{\mu\mu\mu} - m_{\tau} | <20~\MeV/c^2$.
- \item Event selection:
- \begin{itemize}
- \item Preselection of three tracks that combine to give a mass close to $m_{\tau}$, with displaced vertex.
- \item Selection based on three classifiers:
- \begin{itemize}
- \item Geometry and topology ($\mathcal{M}_{3body}$) - multivariate classifier
- \item PID ($\mathcal{M}_{PID}$) - multivariate classifier
- \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 $\PD \to \PK \Ppi \Ppi$ decays.
- \item Evaluation of the upper limit on $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)$ using $CL_s$ method.
- \end{enumerate}
-
-
- \end{frame}
- \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{$\color{white} \tau$ production at LHCb}
- \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{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{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[width=.98\textwidth]{./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{Variables 1/2}
-
- \begin{footnotesize}
-
-
-
-
- The multi-variate classifiers were trained using the following variables:
- \begin{itemize}
- \item \textbf{DOCA:} the minimum of distances of the closest approach of two muons in each of three possible two muon pairings,
- \item \textbf{$\Ptau(\PDs)$ Vertex $\chi^2$:} the quality of the vertex parametrized as the chi square of the $\Ptau$ secondary vertex fit (as defined in,
- \item $\mathbf{c\tau}$\textbf{:} The measured decay length of the $\Ptau$ lepton, assuming its production at the primary vertex. To smooth out the distribution, the
- decay time is transformed according to the formula $T=\exp{(-1000 \cdot \tau )}$,
- \item \textbf{IP $\chi^2$ ($\Ptau$):} $\Ptau$ lepton impact parameter $\chi^2$/ndf,
- \item \textbf{Min.\ IP $\chi^2$ ($\Pmu$):} the minimum value of
- the three $\Pmu$ impact parameter ($\chi^2$/ndf)s,
- \item \textbf{Track $\chi^2$/ndf:} maximum of track's ($\chi^2$)s of the three muons,
-
-
- \end{itemize}
- \end{footnotesize}
- \end{frame}
-
-
-
- \begin{frame}\frametitle{Variables 2/2}
-
- \begin{footnotesize}
-
-
-
-
- The multi-variate classifiers were trained using the following variables:
- \begin{itemize}
-
- \item \textbf{Pointing angle $\alpha$:} the angle between the direction of $\Ptau$ momentum and a straight line from the $\Ptau$ decay vertex to the primary vertex,
- \item $\mathbf{p_T}$: the $\Ptau$ transverse momentum,
- \item \textbf{Track isolation:} the sum of three track isolations variables, each parametrising how far in space is an individual muon candidate w.r.t. the rest of event.
-
- \item \textbf{BDT (Boosted Decision Tree) isolation:} the response of multivariate analysis~(MVA) working at the charged track level and aimed at discriminating between isolated and non-isolated tracks.
- \item \textbf{Cone isolation:} the fraction of the $\Ptau$ candidate transverse
- momentum among the sum of all transverse momenta within a certain cone around the
- $\Ptau$ candidate.
-
- \end{itemize}
- \end{footnotesize}
- \end{frame}
-
-
-
- \begin{frame}\frametitle{Isolations 1/2}
- \begin{footnotesize}
- The track isolation (TI) variable is constructed on the basis of the respective studies performed by the LHCb collaboration for the needs of $B_s^0\to \mu^+ \mu^-$ analysis. The TI is defined as the number of extra tracks (i.e. excluding tracks that are attributed to the $\Ptau \to \mu\mu\mu$ candidate) that can form a vertex with a muon track.
- The assignment to the above SV is based on the selection criteria imposed on the following variables:
- \begin{itemize}
- \item minimum distance between the {\bf\color{red}track} and the PV ({\color{darkpastelgreen}\bf pvdist}),
- \item minimum distance between the {\bf\color{red}track} and the $\Ptau \to \mu\mu\mu$ vertex ({\color{darkpastelgreen}\bf svdist}),
- \item the distance of the closest approach between the {\bf\color{blue}muon} and the {\bf\color{red}track} (DOCA),
- \item IP $\chi^2$,% ($ips$).
- \item angle between the {\bf\color{blue}muon} and the {\bf\color{red}track} ({\color{darkpastelgreen}$\mathbf\beta$}),
- \item the quantity
- \begin{equation}
- f_c=\dfrac{\vert \overrightarrow{p}_{\color{blue}h}+ \overrightarrow{p}_{\color{red}trk} \vert {\color{darkpastelgreen}\alpha^{h + trk, PV}} }
- { \vert \overrightarrow{p}_{\color{blue}h}+ \overrightarrow{p}_{\color{red}trk} \vert {\color{green} \alpha^{h + trk, PV}} + p_{{\rm T},{\color{blue}h}} + p_{{\rm T},{\color{red}trk}} },
- \end{equation}
- where {\color{darkpastelgreen}$\alpha^{h + trk, PV}$} is the angle between the {\bf\color{blue}muon} and the {\bf\color{red}track} candidate, $P_{{\rm T},{\color{blue}h}}$ and $P_{{\rm T},{\color{red}trk}}$ are the transverse momentum with respect to the beam line.
- \end{itemize}
- \end{footnotesize}
-
-
-
- \end{frame}
-
-
-
-
-
- \begin{frame}\frametitle{Isolations 2/2}
- \begin{footnotesize}
- The track is considered as "isolated" if it satisfies the following requirements (imposed on the above mentioned variables):
- \begin{itemize}
- \item pvdist $\in [0.5, 40]~\mm$,
- \item svdist $\in [-0.15,30]~\mm$,
- \item DOCA $< 0.13~\mm$,
- \item Track IP significance $>3$,
- \item $\beta<0.27~\rad$,
- \item $f_c<0.6$.
- \end{itemize}
- %
- %
-
- \centering{
- \includegraphics[width=0.6\textwidth]{LPHNE_iso2.png}
- }
-
-
-
-
- \end{footnotesize}
-
-
-
- \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[width=.95\textwidth]{m3body_2012.pdf}
-
- \end{column}
- \begin{column}{.45\textwidth}
- \begin{itemize}
- \item $\PDs\to\Pphi\Ppi$ decay well modelled in MC.\\
- \includegraphics[width=.9\textwidth]{./dataMC.pdf}
- % \item[$\rightarrow$] i.e.\ also badly pointing non-prompt $\PDs$
- \end{itemize}
- \end{column}
-
- \end{columns}
- \end{frame}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
-
- \frametitle{Signal and background discrimination - $\color{white}{\mathcal{M}_{PID}}$}
- \begin{columns}
- \column{3in}
- \begin{itemize}
- \item $\mathcal{M}_{PID}$ trained using \color{red}{RICH}, \color{blue}{ECAL} and \color{green}{muon chambers}.
- \end{itemize}
-
- \column{2in}
- \includegraphics[width=.98\textwidth]{detcol.png}
- \end{columns}
- \begin{columns}
- \column{0.1in}
- {~}
- \column{2in}
- \includegraphics[width=.95\textwidth]{mPID_2012.pdf}
- \column{3in}
- \begin{itemize}
- \item Trained on signal and background MC.
- \item Calibrated on $\PB \to \PJpsi \PK$ and $\PDs \to \Pphi(\mu\mu) \Ppi$ decays.
- \end{itemize}
- \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}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \begin{frame}
- \frametitle{Binning optimisation}
-
-
- \begin{footnotesize}
- \begin{itemize}
- \item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane.
- \item In 2D we collect the events in groups(bins)
- \item Bins are optimised using $CL_s$ method:
- \begin{equation}
- 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{equation}
- \item The lowest bins are rejected, because they do not contribute to the limit sensitivity.
- \end{itemize}
- \end{footnotesize}
- \begin{columns}
- \column{2.2in}
- \center{2011}\\
- \includegraphics[width=.87\textwidth]{2D_2011.pdf}\\{~}
- \\{~}
- \\{~}\\{~}\\{~}\\{~}
-
- \column{2.2in}
- \center{2012}\\
- \includegraphics[width=.87\textwidth]{2D_2012.pdf}\\{~}
- \\{~}
- \\{~}\\{~}\\{~}\\{~}
-
- \column{0.5in}
- {~}
-
- \end{columns}
-
- \end{frame}
- \begin{frame}
- \frametitle{Impact of 2D 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}
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-
- \section{Normalisation}
-
- \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[width=.97\textwidth]{./Ds_data_2011.pdf}
- \column{2.3in}
- \center{2012}\\
- \includegraphics[width=.97\textwidth]{./Ds_data_2012.pdf}
- \end{columns}
- \end{frame}
-
-
-
-
- \section{Backgrounds}
-
- \begin{frame}
- \frametitle{Misidentification (Peaking background) 1/2}
- \begin{columns}
- \column{3in}
- \begin{itemize}
- \item 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{Misidentification (Peaking background) 2/2}
- \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{Other 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 the $\pm \unit{30}{\MeV}$ 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}
-
-
-
- \section{Model dependence}
-
- \begin{frame}
- \frametitle{Model dependence}
- \begin{itemize}
- \begin{small}
- \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 using Effective Field Theory approach.
- \item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms.
- \end{small}
- \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 remain stable (within $7\,\%$).
- \end{itemize}
- \begin{center}
- \includegraphics[width=.5\textwidth]{./sigDalitz.pdf}
- \end{center}
-
-
- }
- \only<1>{
- \begin{columns}
- \column{0.33\textwidth}
- \includegraphics[width=.78\textwidth]{./LLLL.pdf}\\
- \includegraphics[width=.78\textwidth]{./LLRR.pdf}\\
-
-
- \column{0.33\textwidth}
- \includegraphics[width=.78\textwidth]{./LLLLRAD.pdf}\\
- \includegraphics[width=.78\textwidth]{./LLRRRAD.pdf}
-
- \column{0.33\textwidth}
- \includegraphics[width=.78\textwidth]{./RAD.pdf}\\
- \begin{small}
- \begin{itemize}
- \item All five cases implemented in TAUOLA.
- \item Publication in preparation.
- \end{itemize}
- \end{small}
-
-
- % \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{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{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 First result from hadron collider comparable with B factories.
- \item Since those 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 HFAG 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}
- \begin{align}
- \times \dfrac{\prod_{j=1}^{n} s_iS_i(x_{ij})+b_iB_i(x_{ij})}{\prod_{j=1}^{n_i}B_i(x_{ij})} \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{Summary }
- \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{3.2in}
- \begin{footnotesize}
-
-
- \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.
- \item Erratum to bibliography:
-
-
- \end{itemize}
- \end{footnotesize}
- \column{2in}
- \includegraphics[width=0.93\textwidth]{banana_tau23mu_hfag.pdf}\\
-
-
- \end{columns}
- \begin{footnotesize}
- \begin{itemize}
- \item $\rm[120]$ HFAG report published:arXiv:1412.7515 (previous cited preliminary web report).
- \item $\rm[76]$ accepted for publication in JHEP.
- \end{itemize}
- \end{footnotesize}
- \end{frame}
-
- \pagenumbering{gobble}
-
-
-
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
- \begin{frame}\frametitle{Backup}
-
- \includegraphics[width=0.93\textwidth]{ngbbs4f7918ec8ffb8.jpg}\\
-
-
- \end{frame}
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5555
-
- \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}
-
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%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
-
-
-
-
-
-
-
-
- \end{document}