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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Searches for long-lived light particles at LHCb]{Searches for long-lived light particles at LHCb}
\date{25 September 2015}


\begin{document}
\tikzstyle{every picture}+=[remember picture]

{
\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
\begin{frame}[c]%{\phantom{title page}}
\begin{center}
\begin{center}
	\begin{columns}
		\begin{column}{0.75\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \LARGE {Searches for long-lived light particles at LHCb}
		\end{column}
                \begin{column}{0.02\textwidth}
                  {~}
                  \end{column}
                \begin{column}{0.23\textwidth}
                 % \hspace*{-1.cm}
                  \vspace*{-3mm}
                  \includegraphics[width=0.6\textwidth]{lhcb-logo}
                  \end{column}

	\end{columns}
\end{center}
	\quad
	\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}

\end{column}
\begin{column}{0.53\textwidth}
\includegraphics[height=1.3cm]{uzh-transp}
\end{column}
\end{columns}

\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}{SUSY 2015, Tahoe City, 23-29 August, 2015}

	
\end{center}
\end{frame}
}


%-------------------------------------------------------------------
%                          Introduction
%-------------------------------------------------------------------
%
% Set the background for the rest of the slides.
% Insert infoline
%\setbeamertemplate{background}
% {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}}
%\setbeamertemplate{footline}[bunsentheme]



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\setbeamertemplate{background}
% {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}}
%\setbeamertemplate{footline}[bunsentheme]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\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{Introduction}

\begin{frame}\frametitle{Why long-lived particles?}
\begin{columns}
\column{3in}
\begin{itemize}
\item We all know here that the SM is incomplete.
\item Unfortunately we do no know what is the scale of NP.
\item NP still can come from the Higgs sector $\Rightarrow$ not all properties are yet constrained.
\item There is a long list of theoretical models that predict the existence
of new particles that couple to the SM sector by mixing with the
Higgs.
\end{itemize}

\column{2in}
\includegraphics[width=0.9\textwidth]{susy/NP_couplings.png}


\end{columns}
\begin{itemize}

\item Inflaton, axion-like, dark matter mediator models also predict the
new boson to be light.
\item SUSY models also can have stable long living particles like $\Psquark$, $\Pslepton$.
\end{itemize}


\end{frame}

\begin{frame}
\only<1>{\frametitle{LHCb detector - tracking}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{susy/1050px-Lhcbview.jpg}

\column{2in}
\includegraphics[width=0.95\textwidth]{susy/sketch.png}
\end{columns}
\begin{itemize}
\item Excellent Impact Parameter (IP) resolution ($20~\rm \mu m$).\\
$\Rightarrow$ Identify secondary vertices from heavy flavour decays
\item Proper time resolution $\sim~40~\rm fs$.\\
$\Rightarrow$ Good separation of primary and secondary vertices.
\item Excellent momentum ($\delta p/p \sim 0.4 - 0.6\%$) and inv. mass resolution.\\
$\Rightarrow$ Low combinatorial background.

\end{itemize}


}

\only<2>{\frametitle{LHCb detector - particle identification}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{susy/1050px-Lhcbview.jpg}

\column{2in}
\includegraphics[width=0.95\textwidth]{susy/cher.png}
\end{columns}
\begin{itemize}
\item Excellent Muon identification $\epsilon_{\mu \to \mu} \sim 97\%$, $\epsilon_{\pi \to \mu} \sim 1-3\%$
\item Good $\PK-\Ppi$ separation via RICH detectors, $\epsilon_{\PK \to \PK} \sim 95\%$,  $\epsilon_{\Ppi \to \PK} \sim 5\%$.\\
$\Rightarrow$ Reject peaking backgrounds.
\item High trigger efficiencies, low momentum thresholds.
Muons: $p_T > 1.76 \GeV$ at L0, $p_T > 1.0 \GeV$ at HLT1,\\
$B \to \PJpsi X $: Trigger $\sim 90\%$.

\end{itemize}


}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Data taken by LHCb}
\includegraphics[width=0.9\textwidth]{susy/data.png}

\begin{itemize}
\item In 2011 and 2012 LHCb has gathered $3~{\rm{fb^{-1}}}$ of $pp$ collisions.
\end{itemize}

\end{frame}



\section{Lepton Flavour Violation}
\begin{frame}\frametitle{Lepton Flavour/Number Violation}
\begin{small}
 Lepton Flavour Violation(LFV):
\end{small}


\begin{footnotesize}

After $\Pmuon$ was discovered 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)
\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=0.8\textwidth]{Double_beta_decay_feynman.png}

\end{columns}

\end{footnotesize}
%Double_beta_decay_feynman.png

  % \textref{M.Chrz\k{a}szcz 2014}
\end{frame}


% \section{Lepton Number Violation}
\section{ $\PB$ decays}
\subsection{$\PBminus\to h^{+}\Plepton^{-}\Plepton^{-}$}
\begin{frame}%[t]
\frametitle{LNV in bottom decays}%$\PBminus\to h^{+}\ell^{-}\ell^{-}$}

\only<1>{
\begin{columns}\begin{column}{.5\textwidth}
on-shell neutrino

\includegraphics[width=\textwidth]{pic/B-Majorana2.pdf}
\end{column}
{\begin{column}{.45\textwidth}
virtual neutrino

\includegraphics[width=\textwidth]{pic/B-Majorana1.pdf}
\end{column}
}
\end{columns}
\begin{columns}
\begin{column}{.5\textwidth}
\begin{itemize}
\item resonant production in accessible mass range
\item rates depend on Majorana neutrino--lepton coupling $|V_{\mu 4}|$
\newline {\footnotesize{(e.g.\ \href{http://arxiv.org/abs/0901.3589}{arXiv:0901.3589)}}}
\item $m_4 = m_{\Plepton^{-},\Ppiplus}$
\item $m_{\mu} + m_{\pi} < m_4 < m_{\PB} - m_{\mu}$
\end{itemize}
\end{column}
{
\begin{column}{.5\textwidth}
\begin{exampleblock}{~}
%\begin{itemize}
Diagram without mass restriction
 Cabbibo favoured for $\PB\to\PD$ 
 Analogous to double $\beta$ decay.
%\end{itemize}
\end{exampleblock}
\end{column}
}
\end{columns}
}
 %  \textref{M.Chrz\k{a}szcz 2014}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{Virtual Majorana neutrinos}


\begin{columns}
\only<1>{
\begin{column}{.78\textwidth}
\begin{block}{}
%\begin{itemize}
 $\PBminus\to\PDplus\Pmuon\Pmuon\quad\quad\quad\quad\quad\quad\PBminus\to\PD^{*+}\Pmuon\Pmuon$
%\end{itemize}
\includegraphics[width=\textwidth]{pic/MassFitDp_.pdf}
\end{block}
\end{column}
}


\end{columns}
\only<1>{{
{~}

\begin{columns}
\column{2.5in}
$\quad\mathcal{B}(\PBminus\to\PDplus\Pmuon\Pmuon)<6.9\times 10^{-7}$
\column{2.5in}

$\mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)<2.4\times 10^{-6}$

\end{columns}
}}


 {@ 95\,\% CL}\hspace{.35\textwidth}
 {@ 95\,\% CL}
\\ Based on $0.41~\rm fb^{-1}${~}$7~\TeV$ data.

{~}

\begin{columns}
\begin{column}{6.5cm}
\end{column}
\begin{column}{1.5cm}
%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg}
\end{column}
\begin{column}{4cm}
\hspace{.4cm}

 {\footnotesize{\href{http://prd.aps.org/abstract/PRD/v85/i11/e112004}{\texttt{Phys. Rev.D85 (2012) 112004 }}}}

\end{column}
\end{columns}

%LHCb, arXiv:1201.5600
%\includegraphics[width=.5\textwidth]{UpperAll}
 %  \textref{M.Chrz\k{a}szcz 2014}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{On-shell Majorana neutrinos}
\begin{itemize}
\item $\PBminus \to \Ppiplus \Pmuon \Pmuon$ searched with full data set${~}3~\rm fb^{-1}$.
\item Cut based analysis.
\item Normalization channel $\PBplus \to \PJpsi(\mu\mu)\PKplus$.
\item Searches performed for two scenarios:
\begin{itemize}
\item Short life-time neutrinos: $\tau_4 <1ps$
\item Long life-time neutrinos: $\tau_4  \in (1,1000) ps$
\end{itemize}
\end{itemize}
\begin{columns}

\only<1>{
\includegraphics[width=\textwidth]{Figure2.png}
}

\end{columns}


\begin{columns}
\begin{column}{8.5cm}

\includegraphics[width=\textwidth]{Figure3.png}

\end{column}
\begin{column}{.5cm}
%\includegraphics[width=\textwidth]{pic/LHCb_logo.jpg}
\end{column}

\begin{column}{4cm}
\hspace{.4cm}


 {\footnotesize{\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.131802}{\texttt{Phys. Rev. Lett. 112, 131802 }}}}

\end{column}
\end{columns}


% \textref{M.Chrz\k{a}szcz 2014}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{On-shell Majorana neutrinos}
{~}\\
\begin{columns}
\column{2.5in}
\includegraphics[width=\textwidth]{Figure5.png}\\
\includegraphics[width=\textwidth]{Figure6.png}\\


\column{2.5in}
\begin{small}
\begin{itemize}
\item In absence of signal UL. were set.
\item $Br(\PBminus \to \Ppiplus \Pmuon \Pmuon)$ in range $10^{-9}$.
\item Limits also set for the coupling $| V_{\mu 4} |^2$ 
\end{itemize}
{~}{~}$Br(\PBminus \to \Ppiplus \Pmuon \Pmuon) = \dfrac{G_f^4 f_B^2f_{\pi}^2}{128\pi\hbar }      \tau_B m_B^5 |V_{ub}V_{ud}|^2|V_{\mu4}|^4(1- \dfrac{m_4^2}{m_B^2})\dfrac{m_4}{\Gamma_{N_4}}$
\end{small}
\end{columns}
% \textref{M.Chrz\k{a}szcz 2014}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% johan %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
\frametitle{Summary on LNV in $\color{white} \textbf{B}$ decays}
\vspace{0.5cm}
\begin{columns}
\begin{column}{.65\textwidth}
\begin{footnotesize}
\begin{tabular}{lclr}
channel & limit & & \\\hline
 $\mathcal{B}(\PBminus\to\Ppi^{+}\Pelectron\Pelectron) $     &  $<2.3\times 10^{-8}$     &  @$90\,\%$ CL       &\includegraphics[height=.25cm]{babar}\footnote{BaBar,\href{http://link.aps.org/doi/10.1103/PhysRevD.85.071103}{Phys.\ Rev.\ D \textbf{85}, 071103} (2012)\label{babarB}}\\
 $\mathcal{B}(\PBminus\to\PK^{+}\Pelectron\Pelectron) $     &  $<3.0\times 10^{-8}$     &  @$90\,\%$ CL       &\includegraphics[height=.25cm]{babar}\footnotesize{$^{\text{\ref{babarB}}}$}\\
 $\mathcal{B}(\PBminus\to\PK^{*+}\Pelectron\Pelectron) $    &  $<2.8\times 10^{-6}$    & @$90\,\%$ CL   & \includegraphics[height=.25cm]{cleo}\footnote{CLEO, \href{http://link.aps.org/doi/10.1103/PhysRevD.65.111102}{Phys.\ Rev.\ D \textbf{65}, 111102} (2002)\label{cleolnv}}\\
 $\mathcal{B}(\PBminus\to\Prho^{+}\Pelectron\Pelectron) $    &  $<2.6\times 10^{-6}$    & @$90\,\%$ CL   & \includegraphics[height=.25cm]{cleo}\footnotesize{$^{\text{\ref{cleolnv}}}$}\\
 $\mathcal{B}(\PBminus\to\PD^{+}\Pelectron\Pelectron) $     &  $<2.6\times 10^{-6}$     &  @$90\,\%$ CL       & \includegraphics[height=.25cm]{belle2-logo}\footnote{Belle, \href{http://link.aps.org/doi/10.1103/PhysRevD.84.071106}{Phys.\ Rev.\ D \textbf{84}, 071106(R)}, (2011)\label{bellelnv}}\\
 $\mathcal{B}(\PBminus\to\PD^{+}\Pelectron\Pmuon) $     &  $<1.8\times 10^{-6}$     &  @$90\,\%$ CL       & \includegraphics[height=.25cm]{belle2-logo}\footnotesize{$^{\text{\ref{bellelnv}}}$}\\
%$\mathcal{B}(\PBminus\to\Ppi^{+}\Pmuon\Pmuon)$     &  $<1.3\times 10^{-8}$    &   @$95\,\%$ CL      & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb, CERN-PH-EP-2012-006, \href{http://arxiv.org/abs/1201.5600}{\texttt{arXiv:1201.5600}} (2012)\label{xxxxx}} \\

 $\mathcal{B}(\PBminus\to\PK^{+}\Pmuon\Pmuon) $     &  $<5.4\times 10^{-7}$     &  @$95\,\%$ CL       &\includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb, \href{http://link.aps.org/doi/10.1103/PhysRevLett.108.101601}{Phys.\ Rev.\ Lett.\ 108 101601} (2012)} \\
 %$\mathcal{B}(\PBminus\to\PK^{*+}\Pmuon\Pmuon) $    &  $<4.4\times 10^{-6}$    & @$90\,\%$ CL   & \includegraphics[height=.25cm]{cleo}\footnotesize{$^{\text{\ref{cleolnv}}}$}\\
 %$\mathcal{B}(\PBminus\to\Prho^{+}\Pmuon\Pmuon) $    &  $<5.0\times 10^{-6}$    & @$90\,\%$ CL   & \footnotesize{$^{\text{\ref{cleolnv}}}$}\\
 $\mathcal{B}(\PBminus\to\PD^{+}\Pmuon\Pmuon) $     &  $<6.9\times 10^{-7}$     &  @$95\,\%$ CL       & \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnote{LHCb,Phys. Rev. Lett. (112) 131802 (2014)\label{xxxxx}} \\
 $\mathcal{B}(\PBminus\to\PD^{*+}\Pmuon\Pmuon)$     &  $<2.4\times 10^{-6}$    &   @$95\,\%$ CL      &  \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\
 $\mathcal{B}(\PBminus\to\PDs^{+}\Pmuon\Pmuon)$     &  $<5.8\times 10^{-7}$    &   @$95\,\%$ CL      &  \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\
 $\mathcal{B}(\PBminus\to\PDzero\Ppiminus\Pmuon\Pmuon)$     &  $<1.5\times 10^{-6}$    &   @$95\,\%$ CL      &  \includegraphics[height=.25cm]{pic/LHCb_logo.jpg}\footnotesize{$^{\text{\ref{xxxxx}}}$}\\
\hline
\end{tabular}  %pic/LHCb_logo.jpg
\end{footnotesize}
\end{column}
\end{columns}
%\textref{M.Chrz\k{a}szcz 2014}
\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\PB \to \PKstar \chi(\mu\mu)$ search}
\begin{itemize}
\item Search for displaced di-muon vertex coming form $\PB$ meson.
\end{itemize}
\begin{columns}
\column{2.5in}
\begin{Large}
$\PBzero \to \PKstar \chi( \Pmuon \APmuon)$
\end{Large}
\column{2.5in}
\includegraphics[width=0.9\textwidth]{susy/inflaton.png}
\end{columns}
\begin{itemize}
\item If $\chi$ mixes with the Higgs and it is light:
\begin{itemize}
\item $\Gamma(\PK \to \Ppi \chi) \propto m_t^4 \lambda^5$
\item $\Gamma(\PD \to \Ppi \chi) \propto m_b^4 \lambda^5$
\item $\Gamma(\PB \to \PK \chi) \propto m_t^4 \lambda^2$
\end{itemize}
\item In addition; $\PKstar \to \PK^+ \Ppi^-$ helps in vertex reconstruction.
\item High $\mathcal{B}(\chi \to \Pmuon \APmuon)$. 
\end{itemize}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\PB \to \PKstar \chi(\mu\mu)$ motivation}
Discussed models:
\begin{enumerate}
\item \textbf{Inflaton:} \href{http://arxiv.org/abs/1403.4638}{{\color{blue}{Phys.Lett. B736 (2014) 494}}}
\begin{itemize}
\item $\tau_{\chi} = 10^{-8} - 10^{-10}~s$
\item $m_{\chi} ~\mathcal{O}(1~\GeV)$
\item $\mathcal{B}(\PB \to \PK \chi)~\sim 10^{-6}$
\item effective couplings to SM particles:
\begin{itemize}
\item $g_Y\frac{m_f}{v_{EW}},~g_Y=\sin \theta$
\end{itemize}
\end{itemize}
\item \textbf{Axion portal:} \href{http://arxiv.org/abs/0911.5355}{{\color{blue}{Phys.Rev.D81:034001,2010}}}
\begin{itemize}
\item Prompt decay.
\item Large allowed masses.
\item Axion decay constant: $f_{\chi} \sim 1-3~\TeV$
\begin{itemize}
\item Coupling $\propto \frac{m_f}{f_{\chi}}$.
\end{itemize}
\end{itemize}
\end{enumerate}

All those particles have width much smaller than resolution of LHCb detector.


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Signal properties}
$\Rrightarrow$ Depending on the coupling of the hidden sector we can identify two lifetime regimes:\\{~}

\begin{columns}
\column{0.1in}
{~}
\column{2.5in}
\textbf{Long lifetime} ($>0.2~{\rm{ps}}$)
\begin{itemize}
\item Inflaton \href{http://arxiv.org/abs/0912.0390v2}{{\color{blue}{JHEP 1005:010}}}
\item Displaced vertex.
\item Almost background free.
\item Lower reconstruction efficiency.
\end{itemize}

\column{2.5in}
\textbf{Short lifetime} ($\leq0.2~{\rm{ps}}$)
\begin{itemize}
\item Dark matter mediator \href{http://arxiv.org/abs/1310.6752}{{\color{blue}{	Phys. Lett. B727 }}}
\item Axion \href{http://arxiv.org/abs/0911.5355}{{\color{blue}{Phys.Rev.D81}}}
\item Prompt decay.
\item Contaminated via SM decay.
\end{itemize}

\end{columns}
\begin{columns}
\column{0.1in}
{~}

\column{2.5in}
\includegraphics[width=0.95\textwidth]{susy/displaced.png}

\column{2.5in}
\includegraphics[width=0.95\textwidth]{susy/prompt.png}

\end{columns}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Selection}
\begin{itemize}
\item Trigger on muons.
\item Multivariate selection: ${\rm{\mu BDT}}$ \href{http://arxiv.org/abs/1305.7248}{JINST 8(2013)}
\begin{itemize}
\item ${\rm{\mu BDT}}$ ensures flat efficiency in lifetime of $\chi$.
\end{itemize}
\item Optimized on Punzi figure-of-merit:
\begin{align*}
P_a = \dfrac{S}{\frac{5}{2}+\sqrt{B}},
\end{align*}
with $S$ and $B$ are signal and background yields.
\item Factorize lifetime into two components: $\mathcal{L}=\mathcal{L}^{{\rm{prompt}}}  \bigotimes \mathcal{L}^{{\rm{displaced}}}$
\begin{itemize}
\item Prompt: $\tau < 3\sigma_{\tau}$\\
$\mapsto$ SM background of $\PBzero \to \PKstar \Pmuon \APmuon$
\item Displeased: $\tau > 3\sigma_{\tau}$\\
$\mapsto$ Almost background free.
\end{itemize}
\end{itemize}



\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Search strategy}
\begin{columns}

\column{0.05in}
{~}
\column{3.4in}
\begin{itemize}
\item $\PBzero$ mass constrained.
\item Di-muon mass resolution $\sigma_m  =1 -7~\MeV$.
\item Scan $m_{{\rm test}}$ in steps of $0.5~\sigma_m$.
\begin{itemize}
\item {\color{orange}{Wide resonances}} can't affect the search.
\item {\color{turtlegreen}{Narrows resonances}} we veto.
\end{itemize} 
\item Calculations performed in each $m_{test}$ window.
\end{itemize}
\column{1.6in}
\includegraphics[width=0.9\textwidth]{susy/williams.png}
\end{columns}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Results}

\includegraphics[width=0.95\textwidth]{susy/results.png}

$\Rrightarrow$ Grey regions correspond to vetoed regions where narrow resonances are expected.\\
$\Rrightarrow$ Largest deviation seen in $m_{\chi}=253~\MeV$.\\
$\rightarrowtail$ Not statistically significant: local p-value $=0.2$.\\

$\Rrightarrow$ \href{http://arxiv.org/abs/1508.04094}{\color{blue}{LHCb-PAPER-2015-036}} submited to PRL.

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Branching fraction exclusion limit}

\includegraphics[width=0.95\textwidth]{susy/limit.png}

$\Rrightarrow$ No deviations from background only hypothesis is observed.
\begin{itemize}
\item We set a $95\%$ CL upper limit as function of mass and lifetime of the new particle (in the LHCb accessible range).
\item Lower lifetimes have better limit due to higher reconstruction efficiency.
\end{itemize}


\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Benchmark models}



$\Rrightarrow$ Interpretation of the results in two specific models:\\{~}\\

\includegraphics[width=1.05\textwidth]{susy/benchmarks.png}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Conclusion}
\begin{itemize}
\item A search for a dark boson in the decay channel\\ $\PBzero \to \PKstar \Pmuon \APmuon$ has been presented.
\begin{itemize}
\item No deviations from SM observed.

\end{itemize}
\item Results are the most constraining exclusion limit on the process.
\item LHCb is suited for search for long lived particles.
\item Stay tuned, more searches like this are on they way.

\end{itemize}



\end{frame}


\backupbegin

\begin{frame}\frametitle{Backup}
\topline

\end{frame}

\backupend

\end{document}
