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% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
\usepackage{tikzfeynman}		% For Feynman diagrams
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% http://www.felixl.de/commu.pdf
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minimum height=3em, minimum width=6em]
 
 
 
 
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%% "\alert" is already a beamer pre-defined
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% For shapo's formulas:
\def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
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%\newcommand{\ol}{\overline}
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\def\FL       {\ensuremath{F_{\mathrm{L}}}\xspace}
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\def\ATImPH     {\ensuremath{A_{\mathrm{T,PR}}^{\mathrm{Im}}}\xspace}
\def\ATRePH     {\ensuremath{A_{\mathrm{T,PR}}^{\mathrm{Re}}}\xspace}
\def\FLPH      {\ensuremath{F_{\mathrm{L,PR}}}\xspace}
\def\ATDKG    {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{(2)}}\xspace}
\def\ATImKG     {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{\mathrm{Im}}}\xspace}
\def\ATReKG     {\ensuremath{A_{\mathrm{T,\Kstarz \gamma}}^{\mathrm{Re}}}\xspace}
\def\FLKG       {\ensuremath{F_{\mathrm{L,\Kstarz \gamma}}}\xspace}
\def\ATD     {\ensuremath{A_{\mathrm{T}}^{(2)}}\xspace}
\def\ATIm     {\ensuremath{A_{\mathrm{T}}^{\mathrm{Im}}}\xspace}
\def\ATRe     {\ensuremath{A_{\mathrm{T}}^{\mathrm{Re}}}\xspace}
 
 
 
\newcommand{\disp}{\displaystyle}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
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\def\ea{\end{eqnarray}}
\def\d{\partial}
\def\l{\left(}
\def\r{\right)}
\def\la{\langle}
\def\ra{\rangle}
\def\e{{\rm e}}
\def\Br{{\rm Br}}
 
 
 
\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 Why flavour is important.
\item $\Pbeauty \to \Pstrange \ell \ell$ theory in a nutshell.
\item LHCb measurements of $\Pbeauty \to \Pstrange \ell \ell$.
\item Global fit to $\Pbeauty \to \Pstrange \ell \ell$ measurements.
\item Conclusions.
\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 in explaining dozens of decay rates in the 1960s.
\item There was, however, one 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 skeptical 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 at least a $3 \times 3$ 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 Weak neutral currents were first, introduced in 1958 by Buldman.
\item Later on they were naturally incorporated into unification of weak and electromagnetic interactions.
\item 't Hooft proved that the GWS models was renormalizable.
\item Everything was there on 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 General  Purpose Detectors 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.
\item $q^2$ is the dimuon invariant mass.
 
\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 $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by 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 decay.
 
}
 
\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 $2.8~\sigma$ from SM prediction.
\item Result compatible with previous result.
\end{itemize}
 
 
\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PB \to \PKstar^{\pm} \Pmu \Pmu$}
{~}
\includegraphics[width=0.5\textwidth]{images/ksmumu_BF.png}
\includegraphics[width=0.5\textwidth]{images/kmumu_BF.png}
 
\begin{center}
\begin{columns}
 
\column{0.4\textwidth}
\begin{itemize}
\item Despite large theoretical errors the results are consistently smaller then SM prediction.
\end{itemize}
\column{0.6\textwidth}
\includegraphics[width=0.87\textwidth]{images/bukst_BF.png}
 
 
\end{columns}
 
 
 
 
 
 
 
\end{center}
		\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}
	\only<1>{
	\includegraphics[width=0.65\textwidth]{images/Lb_BR.png}
}
	\only<2>{
	\includegraphics[width=0.45\textwidth]{images/Lblow.png}
\includegraphics[width=0.45\textwidth]{images/Lbhigh.png}
 
}
 
 
	\end{center}
 
 
\begin{itemize}
\item This years LHCb measurement [JHEP 06 (2015) 115]].
\item In total $\sim 300$ candidates in data set.
\item Decay not present in the low $q^2$.
 
\end{itemize}
 
 
 
\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
\begin{frame}{Angular analysis of $\PLambdab \to \PLambda \Pmu \Pmu$}
{~}
	\begin{minipage}{\textwidth}
 
\begin{itemize}
\item For the bins in which we have $>3~\sigma$ significance the forward backward asymmetry for the hadronic and leptonic system.
\end{itemize}
\begin{center}
\includegraphics[width=0.9\textwidth]{{images/AFB_Lb}.png}
\end{center}
\begin{itemize}
\item $A_{FB}^H$ is in good agreement with SM.
\item $A_{FB}^{\ell}$ always in above SM prediction.
\end{itemize}
 
 
\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Lepton universality test}
{~}
	\begin{minipage}{\textwidth}
\begin{columns}
\column{3.0in}
\begin{itemize}
\item If $\PZprime$ is responsible for the $P'_5$ anomaly, does it couple equally to all flavours?
\includegraphics[width=0.9\textwidth]{images/uni2.png}
\item Challenging analysis due to bremsstrahlung.
\item Migration of events modeled by MC.
\item Correct for bremsstrahlung.
\item Take double ratio with $\PBplus \to \PJpsi \PKplus$ to cancel systematics.
\item In $3\invfb$, LHCb measures $R_K=0.745^{+0.090}_{-0.074}(stat.)^{+0.036}_{-0.036}(syst.)$
\item Consistent with SM at $2.6\sigma$.
 
\end{itemize}
\column{2.0in}
\includegraphics[width=0.99\textwidth]{images/RK.png}\\
\begin{itemize}
\item \href{http://arxiv.org/abs/1406.6482}{Phys. Rev. Lett. 113, 151601 (2014)}
\end{itemize}
\end{columns}
 
 
 
\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Angular analysis of $\PBzero \to \PKstar \Pe \Pe$}
{~}
\only<1>{
	\begin{minipage}{\textwidth}
	\begin{itemize}
	\item With the full data set ($3\invfb$) we performed angular analysis in $0.0004 < q^2 <1~\GeV^2$.
	\item Electrons channels are extremely challenging experimentally:
	\begin{itemize}
	\item Bremsstrahlung.
	\item Trigger efficiencies.
	\end{itemize}
	\item Determine the angular observables: $\FL$, $\ATD$, $\ATRe$, $\ATIm$:
	\end{itemize}
\begin{equation}
  \label{eq:physPars}
  \begin{split}
  \FL &=\frac{|A_0|^2}{|A_0|^2+|A_{||}|^2 + |A_\perp|^2}\\
  \ATD &= \frac{|A_\perp|^2-|A_{||}|^2}{|A_\perp|^2+|A_{||}|^2}\\
  \ATRe &= \frac{2\Real(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2}\\
  \ATIm &= \frac{2\Imag(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2},
\end{split}
\end{equation}
 
\end{minipage}
}
\only<2>{
\begin{center}
\includegraphics[width=0.5\textwidth]{images/Kstee.png}\\
\end{center}
\begin{itemize}
\item Results in full agreement with the SM.
\item Similar strength on $C_7$ Wilson coefficient as from $\Pbeauty \to \Pstrange \Pphoton$ decays.
\end{itemize}
 
\begin{center}
\includegraphics[width=0.9\textwidth]{images/Kstee2.png}
\end{center}
 
}
		\vspace*{2.1cm}
\end{frame}
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Theory implications}
{~}
	\begin{minipage}{\textwidth}
\pause
\begin{itemize}
\item A preliminary fit prepared by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}, presented at \href{http://arxiv.org/abs/1510.04239}{\color{blue}{1510.04239}}
\item Took into the fit:
\begin{itemize}
\item $\mathcal{B} ( \PB \to X_s \Pphoton) = (3.36 \pm 0.23) \times 10^{-4} $, Misiak et. al. 2015.
\item $\mathcal{B} ( \PB \to\Pmu \Pmu)$, theory: Bobeth et al 2013, experiment: LHCb+CMS average (2015)
\item $\mathcal{B} ( \PB \to X_s \Pmu \Pmu$), Huber et al 2015
\item $\mathcal{B} ( \PB \to \PK \Pmu \Pmu$),Bouchard et al 2013, 2015
\item $PB_{(s)} \to \PKstar(\Pphi) \Pmu \Pmu$, Horgan et al 2013
\item $\PB \to \PK \Pe \Pe$, $\PB \to \PKstar \Pe \Pe$ and $R_k$.
\end{itemize}
\item Overall there is around $4.5~\sigma$ discrepancy wrt. SM.
\end{itemize}
 
 
 
 
 
\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Theory implications}
{~}
	\begin{minipage}{\textwidth}
 
\begin{itemize}
\item A preliminary fit prepared by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}, presented at \href{http://arxiv.org/abs/1510.04239}{\color{blue}{1510.04239}}
\item The data can be explained by modifying the $C_9$ Wilson coefficient.
\item Overall there is around $4.5~\sigma$ discrepancy wrt. SM.
\end{itemize}
\includegraphics[width=0.9\textwidth]{images/C9.png}
 
 
 
 
\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
 
 
\begin{frame}{Theory implications}
{~}
        \begin{minipage}{\textwidth}
 
\includegraphics[height=0.9\textheight]{images/table.png}
 
 
\end{minipage}
                \vspace*{2.1cm}
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{If not NP?}
{~}
	\begin{minipage}{\textwidth}
\begin{itemize}
\item We are not there yet!
\item There might be something not taken into account in the theory.
\item Resonances ($\PJpsi$, $\Ppsi(2S)$) tails can mimic NP effects.
\item There might be some non factorizable QCD corrections.\\
'' However, the central value of this effect would have to be significantly larger than expected on the basis of existing estimates'' \texttt{D.Straub, 1503.06199}
.
\end{itemize}
\only<1>{
\includegraphics[width=0.9\textwidth]{images/charmloop.png}
}
\only<2>{
\begin{center}
\includegraphics[width=0.6\textwidth]{images/charmloop2.png}
\end{center}
}
 
\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{If not NP?}
{~}
	\begin{minipage}{\textwidth}
\begin{itemize}
\item How about our clean $P_i$ observables?
\item The QCD cancel as mentioned only at leading order.
\item Comparison to normal observables with the optimised ones.
\end{itemize}
\includegraphics[width=0.9\textwidth]{images/C9_S_P.png}
 
 
	\end{minipage}
		\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{There is more!}
{~}
	\begin{minipage}{\textwidth}
 
\begin{itemize}
\item There is one other LUV decay recently measured by LHCb.
\item $R(\PDstar)=\dfrac{\mathcal{B}(\PB \to \PDstar \Ptau \Pnu)}{\mathcal{B}(\PB \to \PDstar \Pmu \Pnu)}$
\item Clean SM prediction: $R(\PDstar)=0.252(3)$, PRD 85 094025 (2012)
\item LHCb result: $R(\PDstar)= 0.336 \pm 0.027 \pm 0.030$, HFAG average: $R(\PDstar)=0.322 \pm 0.022$
\item $3.9~\sigma$ discrepancy wrt. SM.
\end{itemize}
 
\begin{center}
 
\includegraphics[width=0.52\textwidth]{images/RDstar.png}
 
\end{center}
	\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Conclusions}
{~}
	\begin{minipage}{\textwidth}
\begin{itemize}
\item Clear tensions wrt. SM predictions!
\item Measurements cluster in the same direction.
\item We are not opening the champagne yet!
\item Still need improvement both on theory and experimental side.
\item Time will tell if this is QCD+fluctuations or new Physics:
\end{itemize}
\pause
''... when you have eliminated all the\\
Standard Model explanations, whatever remains,\\
however improbable, must be New Physics.''\\
prof. Joaquim Matias
 
	\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
{~}
	\begin{minipage}{\textwidth}
\begin{center}
\begin{LARGE}
Thank you for the attention!
\end{LARGE}
\includegraphics[width=0.8\textwidth]{images/Joke.jpg}
 
\end{center}
 
 
 
	\end{minipage}
		\vspace*{2.1cm}
\end{frame}
 
 
 
\backupbegin
 
\begin{frame}\frametitle{Backup}
\topline
 
\end{frame}
 
\backupend
 
\end{document}