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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Particle Phenomenology, Particle Astrophysics and Cosmology Seminar]{Particle Phenomenology, Particle Astrophysics and Cosmology Seminar}
\date{25 September 2014}


\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}{0.9\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Anomalies in Flavour Physics}
		\end{column}
		\begin{column}{0.2\textwidth}
		  %\includegraphics[width=\textwidth]{SHiP-2}
		\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}{Imperial College \\October 16, 2015}
\end{center}
\end{frame}
}


\begin{frame}{Outline}

	\begin{minipage}{\textwidth}

\begin{enumerate}
\item History of Flavour Physics discoveries.
\item 
\item 
\end{enumerate}	
	
	
	\end{minipage}
		\vspace*{2.cm}
\end{frame}


\begin{frame}{A lesson from history - GIM mechanism}
	\begin{minipage}{\textwidth}

\begin{center}
\includegraphics[width=0.62\textwidth]{images/GIM2.png}
\end{center}
\begin{columns}
\column{0.7\textwidth}
\begin{itemize}
\begin{footnotesize}


\item Cabibbo angle was successful at explaining dozens of decay rates in the 1960s.
\item There was one how ever that was not observed by experiments: $\PKzero \to \Pmuon \APmuon$.
\item Glashow, Iliopoulos, Maiani (GIM) mechanism was proposed in the 1970 to fix this problem. The mechanism required the existence of the $4^{th}$ quark.
\item At that point most of the people were skeptic about that. Fortunately in 1974 the discovery of the $\PJpsi$ meson silenced the skeptics.
\end{footnotesize}
\end{itemize}
\column{0.3\textwidth}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/GIM3.png}\\
\includegraphics[width=0.7\textwidth]{images/604.jpg}\\{~}\\{~}
\end{center}
\end{columns}



\end{minipage}

		\vspace*{2.1cm}
\end{frame}

\begin{frame}{A lesson from history - CKM matrix}
	\begin{minipage}{\textwidth}

\begin{center}
{~}\\{~}\\
\includegraphics[width=0.5\textwidth]{images/CKMmatrix.png}

\end{center}
\begin{columns}
\column{0.6\textwidth}
\begin{itemize}
\begin{small}




\item Similarly CP violation was discovered in 1960s in the neutral kaons decays.
\item $2 \times 2$ Cabbibo matrix could not allow for any CP violation.
\item For the CP violation to be possible one needs atleast $3 \times 3$ unitary matrix \\ $\looparrowright$ Cabibbo-Kobayashi-Maskawa matrix (1973).
\item It predicts existence of $\Pbottom$ (1977) and $\Ptop$ (1995) quarks.
\end{small}

\end{itemize}
\column{0.4\textwidth}
\begin{center}
{~}
%\includegraphics[height=2cm]{images/CP.png}\\
\includegraphics[width=0.96\textwidth]{bottom.jpg}

\end{center}
\end{columns}



\end{minipage}

		\vspace*{2.1cm}
\end{frame}


\begin{frame}{A lesson from history - Weak neutral current}
	\begin{minipage}{\textwidth}

\begin{center}
\includegraphics[height=3cm]{images/weakcurr.png}{~}
\includegraphics[height=3cm]{images/weakcurr2.png}
\end{center}

\begin{columns}
\column{0.6\textwidth}
\begin{itemize}
\begin{small}




\item First the weak neutral currents were introduced in 1958 by Buldman.
\item Later on they were naturally build in unification of weak and electromagnetic interactions.
\item 't Hooft proved that the GWS models was renormalizable. 
\item Everything was there in theory side, only missing piece was the experiment, till 1973.
\end{small}

\end{itemize}
\column{0.4\textwidth}
\begin{center}
{~}
%\includegraphics[height=2cm]{images/CP.png}\\
\includegraphics[width=0.85\textwidth]{images/bubblecern.png}
\end{center}
\end{columns}



\end{minipage}

		\vspace*{2.1cm}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Modern challenges: loops come in to the game}
	\begin{minipage}{\textwidth}
\begin{columns}

\column{0.5\textwidth}
\begin{itemize}
\item Standard Model contributions suppressed or absent:
\begin{itemize}
\item Flavour Changing Neutral Currents.
\item CP violation
\item Lepton Flavour/Number or Lepton Universality violation.
\end{itemize}
\item In general can probe physics beyond GPD reach.
\end{itemize}
\column{0.5\textwidth}
\includegraphics[width=0.99\textwidth]{{images/TauLFV_UL_2014001_averaged}.png}


\end{columns}
\begin{center}
\includegraphics[width=0.75\textwidth]{images/Bsmumu.png}
\includegraphics[width=0.20\textwidth]{{images/bsmumu_SM}.png}
\end{center}
\end{minipage}

		\vspace*{2.1cm}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Recent measurements}
{~}
\only<1>{

	\begin{minipage}{\textwidth}
	
	
\begin{columns}

\column{0.5\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Branching fractions:}}
\begin{description}
\item [$\PB^{0,\pm} \to \PK^{0,\pm} \Pmuon \APmuon$] {~}{~}LHCb, Mar 14
\item [$\PB^{0} \to \PKstar \Pmuon \APmuon$] {~}{~}CMS, Jul 15
\item [$\PBs \to \Pphi \Pmuon \APmuon$] {~}{~}{~}LHCb, Jun 15
\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}LHCb, Sep 15
\item [$\PLambdab \to \PLambda  \Pmuon \APmuon$] {~}{~}{~}{~}LHCb, Mar 15
\item [$\PB \to\Pmuon \APmuon$] {~}{~}{~}{~}{~}CMS+LHCb, Jun 15
\end{description}

$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{CP asymmetry:}}
\begin{description}  
\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}{~}LHCb, Sep 15
\end{description}

$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Isospin asymmetry:}}
\begin{description}  
\item [$\PB \to \PK \Pmuon \APmuon$] {~}{~}{~}{~}{~}LHCb, Mar 14
\end{description}


\column{0.5\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Lepton Universality:}}
\begin{description}  
\item [$\PB^{\pm} \to \PK^{\pm} \Plepton \APlepton$] {~}{~}LHCb, Jun 14
\end{description}


$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Angular:}}
\begin{description}   
\item [$\PB^{0} \to \PK^{\ast} \Plepton \APlepton$] {~}{~}{~}LHCb, Jan 15
\item [$\PB^{\pm} \to \PK^{\ast,\pm} \Plepton \APlepton$] BaBar, Aug 15
\item [$\PBs \to \Pphi \Plepton \APlepton$] {~}{~}{~}LHCb, Jun 15
\item [$\PLambdab \to \PLambda  \Pmuon \APmuon$] {~}{~}LHCb, Mar 15
\end{description}  





\end{columns}

\end{minipage}
}
\only<2>{

	\begin{minipage}{\textwidth}
	
	
\begin{columns}

\column{0.5\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Branching fractions:}}
\begin{description}
\item [{\color{red}{$\PB^{0,\pm} \to \PK^{0,\pm} \Pmuon \APmuon$}}] {~}{~}{\color{red}{LHCb, Mar 14}}
\item [$\PB^{0} \to \PKstar \Pmuon \APmuon$] {~}{~}CMS, Jul 15
\item [{\color{red}{$\PBs \to \Pphi \Pmuon \APmuon$}}] {~}{~}{~}{\color{red}{LHCb, Jun 15}}
\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}LHCb, Sep 15
\item [$\PLambdab \to \PLambda  \Pmuon \APmuon$] {~}{~}{~}{~}LHCb, Mar 15
\item [{\color{red}{$\PB \to\Pmuon \APmuon$}}] {~}{~}{~}{~}{~}{\color{red}{CMS+LHCb, Jun 15}}
\end{description}

$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{CP asymmetry:}}
\begin{description}  
\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}{~}LHCb, Sep 15
\end{description}

$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Isospin asymmetry:}}
\begin{description}  
\item [$\PB \to \PK \Pmuon \APmuon$] {~}{~}{~}{~}{~}LHCb, Mar 14
\end{description}


\column{0.5\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Lepton Universality:}}
\begin{description}  
\item [{\color{red}{$\PB^{\pm} \to \PK^{\pm} \Plepton \APlepton$}}] {~}{~}{\color{red}{LHCb, Jun 14}}
\end{description}


$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Angular:}}
\begin{description}   
\item [{\color{red}{$\PB^{0} \to \PK^{\ast} \Plepton \APlepton$}}] {~}{~}{~}LHCb, Jan 15
\item [{\color{red}{$\PB^{\pm} \to \PK^{\ast,\pm} \Plepton \APlepton$}}] {\color{red}{BaBar, Aug 15}}
\item [$\PBs \to \Pphi \Plepton \APlepton$] {~}{~}{~}LHCb, Jun 15
\item [{\color{red}{$\PLambdab \to \PLambda  \Pmuon \APmuon$}}] {~}{~}{\color{red}{LHCb, Mar 15}}
\end{description}  

\begin{alertblock}{}
$>2~\sigma$ deviations from SM

\end{alertblock}

\end{columns}

\end{minipage}
}

		\vspace*{2.1cm}
\end{frame}

%%%%%%%%%%%%%%%%%%%%5
\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$, where it all begun}
{~}
	\begin{minipage}{\textwidth}
\only<1>{
\begin{columns}
\column{0.6\textwidth}
	August 2013:\\
	
	\includegraphics[width=0.95\textwidth]{images/P5prime.png}
\column{0.4\textwidth}
\begin{itemize}
\item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
\item It turned out that the discrepancy occurred in an observable that was not constrained.  

\end{itemize}
\end{columns}


}




\only<2>{


\begin{columns}
\column{0.6\textwidth}
	August 2013:\\
	
	\includegraphics[width=0.95\textwidth]{images/P5prime.png}
\column{0.4\textwidth}
\begin{itemize}
\item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
\item It turned out that the discrepancy occurred in an observable that was not constrained.  

\end{itemize}
\end{columns}


\begin{exampleblock}{}
Now let's move back and see the theory behind the $\PBzero \to \PKstar \Pmuon \APmuon$ and $P_5^{\prime}$.
\end{exampleblock}
}

\end{minipage}
		\vspace*{2.1cm}
\end{frame}

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



\begin{frame}{Tools in rare $\PBzero$ decays}
{~}
	\begin{minipage}{\textwidth}

\begin{itemize}                                                                                                       
\item \textbf{Operator Product Expansion and Effective Field Theory}                                                  
\end{itemize}                                                                                                         
\begin{columns}                                                                                                       
\column{0.1in}{~}                                                                                                     
\column{3.2in}                                                                                                        
\begin{footnotesize}


\begin{align*}                                                                                                        
H_{eff} = - \dfrac{4G_f}{\sqrt{2}} V V^{\prime \ast}\ \sum_i \left[\underbrace{C_i(\mu)O_i(\mu)}_\text{left-handed} +\
\underbrace{C'_i(\mu)O'_i(\mu)}_\text{right-handed}\right],                                                           
\end{align*}                                                                                                          
                                                                                                                      \end{footnotesize}
\column{2in}                                                                                                          
\begin{tiny}                                                                                                          
\begin{description}                                                                                                   
                \item[i=1,2] Tree                                                                                     
                \item[i=3-6,8] Gluon penguin                                                                          
                \item[i=7] Photon penguin                                                                             
                                \item[i=9.10] EW penguin                                                              
                                \item[i=S] Scalar penguin                                                             
                                \item[i=P] Pseudoscalar penguin                                                       
              \end{description}                                                                                       
                                                                                                                      
\end{tiny}                                                                                                            
\end{columns}                                                                                                         
where $C_i$ are the Wilson coefficients and $O_i$ are the corresponding effective operators.                          
\begin{center}                                                                                                        
\includegraphics[width=0.85\textwidth,height=3cm]{images/all.png}                                                        
                                                                                                                      
\end{center}         





\end{minipage}
		\vspace*{2.1cm}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$ kinematics}
{~}
	\begin{minipage}{\textwidth}
	
$\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decays is described in three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.
	
	\only<1>{	
\begin{columns}	
\column{0.5\textwidth}

$\color{JungleGreen}{\Rrightarrow}$ $\cos \thetak$: the angle between the direction of the kaon in the $\PKstar$ ($\overline{\PKstar}$) rest frame and the direction of the $\PKstar$ ($\overline{\PKstar}$) in the $\PBzero$ ($\APBzero$) rest frame.\\
$\color{JungleGreen}{\Rrightarrow}$ $\cos \thetal$: the angle between the direction of the $\Pmuon$ ($\APmuon$) in the dimuon rest frame and the direction of the dimuon in the $\PBzero$ ($\APBzero$) rest frame.\\
$\color{JungleGreen}{\Rrightarrow}$ $\phi$: the angle between the plane containing the $\Pmuon$ and $\APmuon$ and the plane containing the kaon and pion from the $\PKstar$.



\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/angles.png}

\end{columns}
	}
	\only<2>{
{\tiny{                                                                                                                                                                                                                                        
\eqa{\label{dist}
\frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi}&=&\frac9{32\pi} \bigg[
J_{1s} \sin^2\theta_K + J_{1c} \cos^2\theta_K + (J_{2s} \sin^2\theta_K + J_{2c} \cos^2\theta_K) \cos 2\theta_l\nn\\[1.5mm]
&&\hspace{-2.7cm}+ J_3 \sin^2\theta_K \sin^2\theta_l \cos 2\phi + J_4 \sin 2\theta_K \sin 2\theta_l \cos\phi  + J_5 \sin 2\theta_K \sin\theta_l \cos\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ (J_{6s} \sin^2\theta_K +  {J_{6c} \cos^2\theta_K})  \cos\theta_l    
+ J_7 \sin 2\theta_K \sin\theta_l \sin\phi  + J_8 \sin 2\theta_K \sin 2\theta_l \sin\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ J_9 \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,,
}
}}
$\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decays.

}

\end{minipage}
		\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Transversity amplitudes }
{~}
	\begin{minipage}{\textwidth}

$\color{JungleGreen}{\Rrightarrow}$ One can link the angular observables to transversity amplitudes
{\tiny{
\eqa{
J_{1s}  & = & \frac{(2+\beta_\ell^2)}{4} \left[|\apeL|^2 + |\apaL|^2 +|\apeR|^2 + |\apaR|^2 \right]
    + \frac{4 m_\ell^2}{q^2} \re\left(\apeL\apeR^* + \apaL\apaR^*\right)\,,\nn\\[1mm]
%
J_{1c}  & = &  |\azeL|^2 +|\azeR|^2  + \frac{4m_\ell^2}{q^2} \left[|A_t|^2 + 2\re(\azeL^{}\azeR^*) \right] + \beta_\ell^2\, |A_S|^2 \,,\nn\\[1mm]
%
J_{2s} & = & \frac{ \beta_\ell^2}{4}\left[ |\apeL|^2+ |\apaL|^2 + |\apeR|^2+ |\apaR|^2\right],
\hspace{0.92cm}    J_{2c}  = - \beta_\ell^2\left[|\azeL|^2 + |\azeR|^2 \right]\,,\nn\\[1mm]
%
J_3 & = & \frac{1}{2}\beta_\ell^2\left[ |\apeL|^2 - |\apaL|^2  + |\apeR|^2 - |\apaR|^2\right],
\qquad   J_4  = \frac{1}{\sqrt{2}}\beta_\ell^2\left[\re (\azeL\apaL^* + \azeR\apaR^* )\right],\nn \\[1mm]
%
J_5 & = & \sqrt{2}\beta_\ell\,\Big[\re(\azeL\apeL^* - \azeR\apeR^* ) - \frac{m_\ell}{\sqrt{q^2}}\,
\re(\apaL A_S^*+ \apaR^* A_S) \Big]\,,\nn\\[1mm]
%
J_{6s} & = &  2\beta_\ell\left[\re (\apaL\apeL^* - \apaR\apeR^*) \right]\,,
\hspace{2.25cm} J_{6c} = 4\beta_\ell\, \frac{m_\ell}{\sqrt{q^2}}\, \re (\azeL A_S^*+ \azeR^* A_S)\,,\nn\\[1mm]
%
J_7 & = & \sqrt{2} \beta_\ell\, \Big[\im (\azeL\apaL^* - \azeR\apaR^* ) +
\frac{m_\ell}{\sqrt{q^2}}\, \im (\apeL A_S^* - \apeR^* A_S)) \Big]\,,\nn\\[1mm]
%
J_8 & = & \frac{1}{\sqrt{2}}\beta_\ell^2\left[\im(\azeL\apeL^* + \azeR\apeR^*)\right]\,,
%
\hspace{1.9cm} J_9 = \beta_\ell^2\left[\im (\apaL^{*}\apeL + \apaR^{*}\apeR)\right] \,,
\label{Js}}
}}

\end{minipage}
		\vspace*{2.1cm}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Link to effective operators}
{~}
	\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ So here is where the magic happens. At leading order the amplitudes can be written as:
{\tiny{
\eqa{
\apeLR &=&\sqrt{2} N m_B(1- \hat s)\bigg[  (\Ceff9 + \Cpeff9) \mp (\C{10} + \Cp{10})
+\frac{2\hat{m}_b}{\hat s} (\Ceff7 + \Cpeff7) \bigg]\xi_{\bot}(E_{K^*})  \nn \\[2mm]
\apaLR &=& -\sqrt{2} N m_B (1-\hat s)\bigg[(\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10}) 
+\frac{2\hat{m}_b}{\hat s}(\Ceff7 - \Cpeff7) \bigg] \xi_{\bot}(E_{K^*}) \nn \\[2mm]
\azeLR  &=& -\frac{N m_B (1-\hat s)^2}{2 \hat{m}_{K^*} \sqrt{\hat s}} \bigg[ (\Ceff9 - \Cpeff9)  \mp (\C{10} - \Cp{10}) + 2\hat{m}_b (\Ceff7 - \Cpeff7) \bigg]\xi_{\|}(E_{K^*}),
\label{LargeRecoilAs}}
}}
where $\hat s = q^2 /m_B^2$, $\hat{m}_i = m_i/m_B$. The $\xi_{\|,\bot }$ are the form factors. \\
\pause
$\color{JungleGreen}{\Rrightarrow}$ Now we can construct observables that cancel the $\xi$ form factors at leading order:
\eq{P_5^{\prime} = \dfrac{J_5+\bar{J}_5}{2\sqrt{-(J_2^c+\bar{J}_2^c)(J_2^s+\bar{J}_2^s)} }
}


\end{minipage}
		\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}                                                                                                                    
\only<1>{\frametitle{LHCb detector - tracking}                                                                                   
\begin{columns}                                                                                                                  
\column{3in}                                                                                                                     
\includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}                                                                  
                                                                                                                                 
\column{2in}                                                                                                                     
\includegraphics[width=0.95\textwidth]{images/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]{images/1050px-Lhcbview.jpg}                                                                  
                                                                                                                                 
\column{2in}                                                                                                                     
\includegraphics[width=0.95\textwidth]{images/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}{LHCb update of the $\PBzero \to \PKstar \Pmuon \APmuon$, Selection}
{~}
	\begin{minipage}{\textwidth}
\begin{columns}

\column{0.5\textwidth}
\begin{itemize}
\item PID, kinematics and isolation variables used in a Boosted Decision Tree (BDT) to discriminate signal and background.
\item Reject the regions of $\PJpsi$ and $\Ppsi(2S)$.
\item Specific vetos for backgrounds: $\PLambdab \to \Pproton \PK \Pmu \Pmu$, $\PBs \to \Pphi \Pmu \Pmu$, etc.
\item Using k-Fold technique and signal proxy $\PB \to \PJpsi \PKstar$ for training the BDT. 
\item Improved selection allowed for finer binning than the $1\invfb$ analysis.
\end{itemize}


\column{0.5\textwidth}

\includegraphics[width=0.88\textwidth]{images/Fig1.pdf} \\
\includegraphics[width=0.88\textwidth]{images/fold.png}

\end{columns}



\end{minipage}
		\vspace*{2.1cm}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{LHCb update of the $\PBzero \to \PKstar \Pmuon \APmuon$, Selection}
{~}
	\begin{minipage}{\textwidth}

\begin{itemize}
\item Signal modelled by a sum of two Crystal-Ball functions.
\item Shape is defined using $\PB \to \PJpsi \PKstar$ and corrected for $q^2$ dependency.
\item Combinatorial background modelled by exponent.
\end{itemize}

\begin{columns}
\column{0.5\textwidth}
\begin{itemize}
\item $\PK \Ppi$ system:
\begin{itemize}
\item Rel. Breit Wigner for P-wave
\item Lass model for the S-wave.
\item Linear model for background.
\end{itemize}
\end{itemize}

\column{0.5\textwidth}

\includegraphics[width=0.88\textwidth]{images/pbkg}

\end{columns}

\begin{large}
\begin{itemize}
\item In total we found $2398\pm57$ candidates in the $0.1-19~\GeV^2$ $q^2$ region.
\item $624 \pm 30$ candidates in the theoretically the most interesting $1.1-6.0~\GeV^2$ region.
\end{itemize}
\end{large}




\end{minipage}
		\vspace*{2.1cm}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Detector acceptance}
{~}
	\begin{minipage}{\textwidth}
\begin{columns}

\column{0.6\textwidth}
\begin{itemize}
\item Detector distorts our angular distribution.
\item We need to model this effect.
\item 4D function is used:
\begin{align*}
\epsilon (\cos \thetal, \cos \thetak, \phi, q^2) = \\\sum_{ijkl} P_i(\cos \thetal) P_j(\cos \thetak ) P_k(\phi) P_l(q^2),
\end{align*}
where $P_i$ is the Legendre polynomial of order $i$.
\item We use up to $4^{th}, 5^{th}, 6^{th}, 5^{th}$ order for the $\cos \thetal, \cos \thetak, \phi, q^2$. 
\end{itemize}




\column{0.4\textwidth}
\includegraphics[width=0.99\textwidth]{images/det.png}
\end{columns}


\end{minipage}
		\vspace*{2.1cm}
\end{frame}

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


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Control channel}
{~}
	\begin{minipage}{\textwidth}


\begin{itemize}
\item We tested our unfolding procedure on $\PB \to \PJpsi \PKstar$.
\item The result is in perfect agreement with other experiments and our different analysis of this decay.
\end{itemize}

\begin{columns}

\column{0.5\textwidth}

\includegraphics[width=0.95\textwidth]{images/mlogjpsi.png}
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/mkpijpsi.png}

\end{columns}


\includegraphics[width=0.99\textwidth]{images/angles2.png}



\end{minipage}
		\vspace*{2.1cm}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Results in $\PB to \PKstar \Pmu \Pmu$}
	\begin{minipage}{\textwidth}
	\begin{center}
	\includegraphics[angle=-90,width=0.65\textwidth]{images/Fig17.pdf}\\
	\end{center}

\begin{itemize}
\item Tension with $3~\invfb$ gets confirmed!
\item The two bins deviate both in $2.8~\sigma$ form SM prediction.
\item Result compatible with previous result.
\end{itemize}


\end{minipage}
		\vspace*{2.1cm}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PBs \to \Pphi \Pmu \Pmu$}
{~}
	\begin{minipage}{\textwidth}
	\begin{center}
	\includegraphics[width=0.65\textwidth]{images/bs2phipi.png}\\
	\end{center}

\begin{itemize}
\item Recent LHCb measurement [JHEPP09 (2015) 179].  
\item Suppressed by $\frac{f_s}{f_d}$.
\item Cleaner because of narrow $\Pphi$ resonance.
\item $3.3~\sigma$ deviation in SM in the $1-6\GeV^2$ bin.
\end{itemize}


\end{minipage}
		\vspace*{2.1cm}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PBs \to \Pphi \Pmu \Pmu$}
{~}
	\begin{minipage}{\textwidth}
	\begin{center}
	\includegraphics[width=0.65\textwidth]{images/bs2phipi.png}\\
	\end{center}

\begin{itemize}
\item Recent LHCb measurement [JHEPP09 (2015) 179].  
\item Suppressed by $\frac{f_s}{f_d}$.
\item Cleaner because of narrow $\Pphi$ resonance.
\item $3.3~\sigma$ deviation in SM in the $1-6\GeV^2$ bin.
\end{itemize}


\end{minipage}
		\vspace*{2.1cm}
\end{frame}


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

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PLambdab \to \PLambda \Pmu \Pmu$}
{~}
	\begin{minipage}{\textwidth}
	\begin{center}
	\includegraphics[width=0.65\textwidth]{images/Lb_BR.png}
	\end{center}

\begin{itemize}
\item Recent LHCb measurement [JHEPP09 (2015) 179].  
\item Suppressed by $\frac{f_s}{f_d}$.
\item Cleaner because of narrow $\Pphi$ resonance.
\item $3.3~\sigma$ deviation in SM in the $1-6\GeV^2$ bin.
\end{itemize}


\end{minipage}
		\vspace*{2.1cm}
\end{frame}



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\begin{frame}\frametitle{Backup}
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\end{document}
