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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz, Nazila Mahmoudi} }
\institute{UZH}
\title[Reinterpretation of Flavour Constraints]{Reinterpretation of Flavour Constraints}
\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}{0.95\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {(Re)interpretation of Flavour Constraints}
		\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{2em}




{\fontspec{Trebuchet MS} \Large Marcin Chrząszcz}\\
University of Zurich \&  Polish Academy of Sciences\\
	\vspace{1em}
{\fontspec{Trebuchet MS} \Large Nazila Mahmoudi}\\
Lyon University \& CERN TH

\vspace{1em}
		\footnotesize\textcolor{gray}{In Collaboration with:\\}\normalsize
		F. Bernlochner, P. Jackson, P.Scott, M.White, N.Serra
\vspace{3.5em}

	\textcolor{normal text.fg!50!Comment}{(Re)interpreting the results of new physics searches at the LHC\\CERN, December 12, 2016}
\end{center}
\end{frame}
}


\begin{frame}[c]{Outline}
	\begin{minipage}{\textwidth}

\ARROW Theoretical framework for $B$ decays\\[3.mm]
\ARROW $B \to K^* \ell^+ \ell^-$ observables and calculations\\[3.mm]
\ARROW Which data do Flavour factories publish\\[3.mm]
\ARROW New Physics searches\\[3.mm]
\ARROW What would be the best way to exchange the information?\\[3.mm]
\ARROW Wilson Coefficients fits with \textbf{GAMBIT}\\[3.mm]
\ARROW Questions for discussion
	
	\end{minipage}
		\vspace*{2.cm}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%
% Nazila
%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\begin{center}
\begin{Huge}
Theoretical framework for $\PB$ decays.
\end{Huge}
\end{center}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Theoretical framework for $B$ decays}
\begin{footnotesize}
\vspace*{0.2cm}\hspace*{0.2cm}{\color{brique} \Large A multi-scale problem}\vspace*{0.2cm} 
\begin{itemize} 
\item new physics: $\Lambda_{\mathrm{NP}}\gtrsim$ TeV\vspace*{0.05cm}
\item electroweak interactions: $M_W\sim 80$ GeV\vspace*{0.05cm}
\item hadronic effects: $m_b\sim 5$ GeV\vspace*{0.05cm}
\item QCD interactions: $\Lambda_{\mathrm{QCD}}\sim 0.2$ GeV\vspace*{0.2cm}
\end{itemize}\pause
\hspace*{2.cm}{\color{brique} \Large $\Rightarrow$ Effective field theory approach:\\}\vspace*{0.1cm} 
\hspace*{1.cm}{\color{brique}separation between low and high energies using Operator Product Expansion} \vspace*{0.2cm}
\begin{itemize} 
\item short distance: Wilson coefficients, computed perturbatively\vspace*{0.cm}
\item long distance: local operators
\end{itemize}

\begin{center}
{\color{darkblue}$\displaystyle {\cal H}_{\rm eff}  =  -\frac{4G_{F}}{\sqrt{2}} V_{tb} V_{ts}^{*} \, \Bigl(\,\sum_{i=1\cdots10,S,P} \bigl(C_{i}(\mu) \mathcal{O}_i(\mu)+C'_{i}(\mu) \mathcal{O}'_i(\mu)\bigr)\Bigr)$}
\end{center}
\vspace*{1mm}\pause
\hspace*{2mm} New physics:\\[1mm]
\begin{itemize}
 \item Corrections to the Wilson coefficients: $C_{i} \rightarrow C_{i}+{\color{brique}\Delta C_{i}^{NP}}$
 \item Additional operators: ${\color{brique}\displaystyle\sum_{j} C_{j}^{NP}\mathcal{O}_j^{NP}}$
\end{itemize}

\end{footnotesize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame { \frametitle{$\mathcal{O}$perators}
\begin{footnotesize}

\vspace*{-0.3cm}
\begin{columns} 
\begin{column}[c]{0.3cm}
~
\end{column}
\begin{column}[c]{6.6cm}
$\mathcal{O}_1 = (\bar{s} \gamma_{\mu} T^a P_L c)(\bar{c} \gamma^{\mu} T^a P_L b)$\\
$\mathcal{O}_2 = (\bar{s} \gamma_{\mu} P_L c)(\bar{c} \gamma^{\mu} P_L b)$\\[1.cm]
$\mathcal{O}_3 = (\bar{s} \gamma_{\mu} P_L b) {\sum_q} (\bar{q} \gamma^{\mu} q)$\\
$\mathcal{O}_4 = (\bar{s} \gamma_{\mu} T^a P_L b) {\sum_q} (\bar{q} \gamma^{\mu} T^a q)$\\   
$\mathcal{O}_5 = (\bar{s} \gamma_{\mu_1}\gamma_{\mu_2}\gamma_{\mu_3} P_L b) {\sum_q} (\bar{q} \gamma^{\mu_1}\gamma^{\mu_2}\gamma^{\mu_3} q)$\\
$\mathcal{O}_6 = (\bar{s} \gamma_{\mu_1}\gamma_{\mu_2}\gamma_{\mu_3} T^a P_L b) {\sum_q} (\bar{q} \gamma^{\mu_1}\gamma^{\mu_2}\gamma^{\mu_3} T^a q)$\\[0.5cm]
$\mathcal{O}_7 = \frac{e}{16\pi^2} \Big[ \bar{s} \sigma^{\mu \nu} (m_s P_L + m_b P_R) b \Big] F_{\mu \nu}$\\
$\mathcal{O}_8 = \frac{g}{16\pi^2} \Big[ \bar{s} \sigma^{\mu \nu} (m_s P_L + m_b P_R) T^a b \Big] G_{\mu \nu}^a$\\[1.cm]
$\mathcal{O}_9 = \frac{e^2}{(4\pi)^2} (\overline{s} \gamma^\mu b_L) (\bar{l} \gamma_\mu l)$\\
$\mathcal{O}_{10} = \frac{e^2}{(4\pi)^2} (\overline{s} \gamma^\mu b_L) (\bar{l} \gamma_\mu \gamma_5 l)$
\end{column}
\begin{column}[c]{5.cm}
\begin{center}
\includegraphics[height=1.7cm]{O1O2.png}\\[0.3cm]
\includegraphics[height=1.7cm]{QCDpenguins.png}
\includegraphics[height=1.7cm]{EWpenguins.png}\\[0.3cm]
\includegraphics[height=1.7cm]{O7O8.png}\\[0.3cm]
\includegraphics[height=1.7cm]{O9O10.png}
\end{center}
\end{column}
\end{columns}
\end{footnotesize}

}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame { \frametitle{Wilson coefficients}
%
\begin{footnotesize}

\begin{columns} 
\begin{column}[c]{11.4cm} 
{\large\bf\color{brique}Two main steps:}
\vspace*{0.4cm}
\begin{itemize}
 \item Calculating $C^{eff}_i(\mu)$ at scale $\mu \sim M_W$ by requiring matching between the effective and full theories
{\color{vert}\begin{equation*}
C^{eff}_i(\mu) = C^{(0)eff}_i(\mu) + \dfrac{\alpha_s(\mu)}{4 \pi} C^{(1)eff}_i(\mu) + \cdots
\end{equation*}}
%
\item Evolving the $C^{eff}_i(\mu)$ to scale $\mu \sim m_b$ using the RGE:
{\color{vert}\begin{equation*}
\mu \dfrac{d}{d \mu} C_i^{eff}(\mu) = C_j^{eff}(\mu) \gamma^{eff}_{ji}(\mu)
\end{equation*}}
%
driven by the anomalous dimension matrix $\hat{\gamma}^{eff}(\mu)$\\[0.5cm]
% {\color{vert}\begin{equation*}
% \hat{\gamma}^{eff}(\mu) = \dfrac{\alpha_s (\mu)}{4 \pi} \hat{\gamma}^{(0)eff}  
%                         + \dfrac{\alpha_s^2(\mu)}{(4 \pi)^2} \hat{\gamma}^{(1)eff} + \cdots 
% \end{equation*}}
\end{itemize}
SM contributions to $C_i(\mu_b)$ are known to NNLO QCD and NLO EW/QED
\end{column}
\end{columns}
\end{footnotesize}

}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame { \frametitle{Hadronic quantities}
\begin{footnotesize}

\begin{columns} 
\begin{column}[c]{10.cm} 
{\bf To compute the amplitudes:}\\[0.1cm]
\hspace*{1.cm}$\mathcal{A}(A \to B)= \langle B|{\cal H}_{\rm eff}|A \rangle = \frac{G_F}{\sqrt2} \sum_i \lambda_i C_i(\mu) \langle B|\mathcal{O}_i|A \rangle (\mu)$\\[0.2cm]

{\color{brique}$\langle B|\mathcal{O}_i|A \rangle$: hadronic matrix element}\\[0.6cm]

{\bf How to compute matrix elements?}\\[0.1cm]
\hspace*{0.5cm}$\rightarrow$ Model building, Lattice simulations, Light flavour symmetries, Heavy flavour symmetries, ...\\[0.1cm]
\hspace*{0.5cm}$\rightarrow$ Describe hadronic matrix elements in terms of {\bf hadronic quantities}\\[0.7cm]

{\bf Two types of hadronic quantities:}\\[0.1cm]
\begin{itemize}
\item {\color{brique}\bf Decay constants}: {\small Probability amplitude of hadronising quark pair into a given hadron}\\[0.1cm]
\item {\color{brique}\bf Form factors}: {\small Transition from a meson to another through flavour change}
\end{itemize}
\end{column}
\end{columns}

\end{footnotesize}

}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame { \frametitle{$B \to K^* \ell^+ \ell^-$ -- Angular distributions}
\begin{footnotesize}

{\color{brique}\bf Angular distributions}
\begin{columns} 
\begin{column}[c]{7.cm}
The full angular distribution of the decay $\bar{B}^{0} \to \bar K^{*0} \ell^+ \ell^-$ ($\bar K^{*0} \to K^- \pi^+$) is completely described by four independent kinematic variables:\\ {\color{brique}$q^2$} (dilepton invariant mass squared), {\color{brique}$\theta_\ell$, $\theta_{K^*}$, $\phi$}\\
\end{column}
\begin{column}[c]{5.cm}
\begin{center}
\begin{figure}[pb]  
\vspace*{-1.3cm}\hspace*{-0.7cm}\includegraphics[width=6.cm]{angulardist2.png}\\[0.cm]
\end{figure}
\end{center}
\end{column}
\end{columns}
\pause
\begin{columns}
\begin{column}[c]{0.2cm}
~\end{column}
\begin{column}[c]{8.cm}
Main operators:\\[0.2cm]
$\mathcal{O}_9= \frac{e^2}{(4\pi)^2} (\overline{s} \gamma^\mu b_L) (\bar{\ell} \gamma_\mu \ell)$,
\hspace*{0.14cm}$\mathcal{O}_{10}= \frac{e^2}{(4\pi)^2} (\overline{s} \gamma^\mu b_L) (\bar{\ell} \gamma_\mu \gamma_5 \ell) $\\[0.cm]
% $\mathcal{O}_S=\frac{e^2}{16\pi^2}(\bar{s}^{\alpha}_Lb^{\alpha}_R)(\bar{\ell}\,\ell)$,
% \hspace*{0.6cm}$\mathcal{O}_P=\frac{e^2}{16\pi^2}(\bar{s}^{\alpha}_Lb^{\alpha}_R)(\bar{\ell}\gamma_5 \ell)$
\end{column}
\begin{column}[c]{5.cm}
\begin{center}
\visible<2>{\hspace*{-1.2cm}\includegraphics[width=2.cm]{bkmumu1.pdf}~\includegraphics[width=2.cm]{bkmumu2.pdf}}
\end{center}
\end{column}
\end{columns}
{\vspace*{-0.1cm}\hspace*{1.cm}\tiny \bf \color{vert} F. Kruger et al., Phys. Rev. D 61 (2000) 114028;\\[-0.1cm] 
\hspace*{1.cm}W. Altmannshofer et al., JHEP 0901 (2009) 019; U. Egede et al., JHEP 1010 (2010) 056}\\[0.2cm]

{\color{brique}\bf Differential decay distribution:}
\begin{equation*}
\frac{d^4\Gamma}{dq^2\, d\cos{\color{brique}\theta_\ell}\, d\cos{\color{brique}\theta_{V}}\, d{\color{brique}\phi}} =
   \frac{9}{32\pi} {\color{blue}J}(q^2, {\color{brique}\theta_\ell}, {\color{brique}{\color{brique}\theta_{V}}}, {\color{brique}{\color{brique}\phi}})
\end{equation*}

${\color{blue}J}(q^2, {\color{brique}\theta_\ell}, {\color{brique}\theta_V}, {\color{brique}\phi}) = \sum_i {\color{blue}J_i}(q^2) \, f_i({\color{brique}\theta_\ell}, {\color{brique}\theta_V}, {\color{brique}\phi})$ \\[0.1cm]

\hspace*{3.3cm}{ $^\searrow$ angular coefficients ${\color{blue}J_{1-9}}$}\\[0.cm]
\hspace*{3.3cm}{$^\searrow$ functions of the transversity amplitudes $A_0$, $A_\parallel$, $A_\perp$, $A_t$, and $A_S$, Transversity amplitudes: functions of Wilson coefficients and form factors}
\end{footnotesize}

}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame { \frametitle{$B \to K^* \ell^+ \ell^-$ -- Amplitudes}
\begin{footnotesize}

A closer look to the Effective Hamiltonian:
\[
  {\cal H}_{\rm eff} = {\cal H}_{\rm eff}^{\rm had} + {\cal H}_{\rm
      eff}^{\rm sl} \nonumber
\]
% \hspace*{5.5cm}{\small ``Naive'' factorisation of leptonic and hadronic parts}\\[0.1cm]
\[
  {\cal H}_{\rm eff}^{\rm sl} = - \frac{4 G_F}{\sqrt{2}} V_{tb}V_{ts}^{*} \Big[
         \sum_{i=7,9,10} C_i^{(\prime)} O_i^{(\prime)} \Big]\nonumber
\]
$\langle \bar{K}^* | {\cal H}_{\rm eff}^{\rm sl} | \bar{B}  \rangle$: \textcolor{darkgreen}{$B \to K^*$ form factors $V, A_{0,1,2}, T_{1,2,3}$} \\[0.1cm]
Transversity amplitudes:
\begin{align*}
 A_\perp^{L,R} &\simeq N_\perp \left\{ ({\color{orange}C_9^{+}}\mp {\color{orange}C_{10}^{+}}) \frac{\textcolor{darkgreen}{V(q^2)}}{m_B+m_{K^*}} +\frac{2m_b}{q^2} {\color{orange}C_7^{+}} \textcolor{darkgreen}{T_1(q^2)} \right\} \nonumber\\ 
 A_\parallel^{L,R} &\simeq N_\parallel \left\{ ({\color{orange}C_9^{-}}\mp {\color{orange}C_{10}^{-}}) \frac{\textcolor{darkgreen}{A_1(q^2)}}{m_B-m_{K^*}} +\frac{2m_b}{q^2} {\color{orange}C_7^{-}} \textcolor{darkgreen}{T_2(q^2)} \right\} \nonumber\\ 
 A_0^{L,R} &\simeq N_0 \Big\{ ({\color{orange}C_9^{-}}\mp {\color{orange}C_{10}^{-}})\left[ (\ldots)\textcolor{darkgreen}{A_1(q^2)}+(\ldots)\textcolor{darkgreen}{A_2(q^2)} \right]\nonumber \\ 
           &\qquad \qquad+2m_b {\color{orange}C_7^{-}}\left[ (\ldots)\textcolor{darkgreen}{T_2(q^2)}+(\ldots)\textcolor{darkgreen}{T_3(q^2)} \right] \Big\} \nonumber \\ 
 A_S &= N_S ({\color{orange}C_S}- {\color{orange}C_S^\prime})\textcolor{darkgreen}{A_0 (q^2)} \nonumber
 \end{align*}
\vspace*{-0.6cm}\[ {\color{gray} \hspace*{4.cm}\left( C_{i}^\pm \equiv C_i \pm C_i^\prime \right)} \nonumber\]
\end{footnotesize}

}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame { \frametitle{$B \to K^* \ell^+ \ell^-$ -- Amplitudes}
\begin{footnotesize}

\vspace*{0.12cm}A closer look to the Effective Hamiltonian:
\[
  {\cal H}_{\rm eff} = {\cal H}_{\rm eff}^{\rm had} + {\cal H}_{\rm
      eff}^{\rm sl} \nonumber
\]
\vspace*{-0.3cm}
\[
  {\cal H}_{\rm eff}^{\rm had} =
     -\frac{4 G_F}{\sqrt{2}} V_{tb}V_{ts}^{*} \left[
       \sum_{i=1\dots 6} C_i O_i + C_{8}O_{8} \right] 
\]
\begin{align*}\nonumber
\mathcal A^{\rm (had)}_\lambda = &- i \frac{e^2}{q^2}  {\color{red}\int \!\! d^4x e^{- i q \cdot x}
   \langle \ell^+ \ell^- | j_\mu^{\rm em, lept}(x) | 0 \rangle} \\ \nonumber
 &\times {\color{blue} \int \!\! d^4 y\, e^{i q \cdot y}   \langle \bar{K}^*_\lambda | T \{ j^{\rm em, had, \mu}(y)
 {\mathcal H}^{\rm had}_{\rm eff}(0) \} | \bar B \rangle}\\ \nonumber
\equiv &\frac{e^2}{q^2} \epsilon_\mu{\color{red} L_V^\mu }  \Big[ \underbrace{ {\color{blue} {\rm LO \; in} \; {\cal O}(\frac{\Lambda}{m_b},\frac{\Lambda}{E_{K^*}})}}_{\parbox{2.3cm}{\small Non-Fact., QCDf
%\\ {\tiny \bf \color{vert}Beneke et al., 0106067; 0412400}
}} +\underbrace{{\color{blue} ~~~h_\lambda(q^2)~~~}}_{\parbox{2.cm}{\footnotesize power corrections\\[0.1cm] \visible<2->{$\to$ {\bf unknown}
%\\ {\tiny \bf \color{vert}partial calculation:\\ Khodjamirian et al.,\\ 1006.4945}
}}} \Big]
  \end{align*}%
\vspace*{0.1cm}
\visible<3>{%
\begin{center}
{\small The observed deviations from the SM can be explained with 20-50\% non-factorisable power corrections at the
observable level {\tiny \bf \color{vert}(Ciuchini et al., 1512.07157)}\\[0.2cm]
This corresponds to more than 150\% error at the amplitude level for the critical bins!}
\end{center}
}
\vspace*{0.35cm}
\end{footnotesize}

}


\frame { \frametitle{$B \to K^* \mu^+ \mu^-$ -- Optimized observables}
\begin{align*}
%
\av{P_1}_{\rm bin}&= \frac12 \frac{\int_{{\rm bin}} dq^2 [J_3+\bar J_3]}{\int_{{\rm bin}} dq^2 [J_{2s}+\bar J_{2s}]}
& 
% \av{P_1^{CP} }_{\rm bin}&= \frac12 \frac{\int_{{\rm bin}} dq^2 [J_3-\bar J_3]}{\int_{{\rm bin}} dq^2 [J_{2s}+\bar J_{2s}]}\ ,\label{p1}\\
%
\av{P_2}_{\rm bin} &= \frac18 \frac{\int_{{\rm bin}} dq^2 [J_{6s}+\bar J_{6s}]}{\int_{{\rm bin}} dq^2 [J_{2s}+\bar J_{2s}]}\\
% & \av{P_2^{CP} }_{\rm bin} &= \frac18 \frac{\int_{{\rm bin}} dq^2 [J_{6s}-\bar J_{6s}]}{\int_{{\rm bin}} dq^2 [J_{2s}+\bar J_{2s}]}\ ,\\
%
% \av{P_3}_{\rm bin} &= -\frac14 \frac{\int_{{\rm bin}} dq^2 [J_9+\bar J_9]}{\int_{{\rm bin}} dq^2 [J_{2s}+\bar J_{2s}]}\ ,
% & \av{P_3^{CP} }_{\rm bin} &= -\frac14 \frac{\int_{{\rm bin}} dq^2 [J_9-\bar J_9]}{\int_{{\rm bin}} dq^2 [J_{2s}+\bar J_{2s}]}\ ,\\
%
\av{P'_4}_{\rm bin} &= \frac1{{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_4+\bar J_4]
& 
% \av{{P'_4}^{CP} }_{\rm bin} &= \frac1{{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_4-\bar J_4]\ ,\\
%
\av{P'_5}_{\rm bin} &= \frac1{2{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_5+\bar J_5]\\
% & \av{{P'_5}^{CP} }_{\rm bin} &= \frac1{2{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_5-\bar J_5]\ ,\\
%
\av{P'_6}_{\rm bin} &= \frac{-1}{2{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_7+\bar J_7]
& 
% \av{{P'_6}^{CP} }_{\rm bin} &= \frac{-1}{2{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_7-\bar J_7]\ ,\\
%
\av{P'_8}_{\rm bin} &= \frac{-1}{{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_8+\bar J_8]
% & \av{{P'_8}^{CP} }_{\rm bin} &= \frac{-1}{{\cal N}_\bin^\prime} \int_{{\rm bin}} dq^2 [J_8-\bar J_8]\ .
%
\end{align*}
%
% where the normalization ${\cal N}_\bin^\prime$ is defined as
%
with {\footnotesize \[{\cal N}_\bin^\prime = {\textstyle \sqrt{-\int_\bin dq^2 [J_{2s}+\bar J_{2s}] \int_{{\rm bin}} dq^2 [J_{2c}+\bar J_{2c}]}}\]}\\[6mm]
$+$ CP violating clean observables and other combinations\\[2mm]
{\vspace*{-0.cm}\hspace*{5.cm}\tiny \bf \color{vert}U.~Egede et al., JHEP {\bf 0811} (2008) 032, JHEP {\bf 1010} (2010) 056}\\
{\vspace*{-0.1cm}\hspace*{5.cm}\tiny \bf \color{vert}J.~Matias et al., JHEP {\bf 1204} (2012) 104}\\
{\vspace*{-0.1cm}\hspace*{5.cm}\tiny \bf \color{vert}S.~Descotes-Genon et al., JHEP 1305 (2013) 137}\\
% Sebastien Descotes-Genon (Orsay, LPT), Tobias Hurth (Mainz U., Inst. Phys.), Joaquim Matias, Javier Virto, JHEP 1305 (2013) 137
}

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


%%%%%%%%%%%%%%%%%%%%%%
% Marcin
%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
Flavour measurements
\end{Huge}
\end{center}

\end{frame}
\begin{frame}\frametitle{Detector effects 1/2}
{~}\\
\ARROW In Flavour factories because we usually measure the properties of a $\PB$ meson decay we can 
provide the measurements that are corrected for the detector effects!\\
\begin{center}
\includegraphics[width=0.95\textwidth]{images/andy.png}\let\thefootnote\relax\footnote
{Thanks to Andy Buckley for the plot.}
\end{center}
\ARROW The differences that ''Reco recovery'' doesn't recover are recovered at the analysis stage.\\
\ARROW Some imperfections (usually small), are assigned as systematics!


\end{frame}

\begin{frame}\frametitle{Detector effects 2/2}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}

\ARROW For example: measurement of angular coefficients of $\PB \to \PKstar \Pmu \Pmu$, \href{https://arxiv.org/abs/1512.04442}{\color{blue}arXiv::1512.04442}, \href{https://arxiv.org/abs/1604.04042}{\color{blue}arXiv::1604.04042}

\only<1>{
\begin{center}
\includegraphics[width=0.75\textwidth]{images/acc.png}
\end{center}
}
\only<2>{
\begin{center}
\includegraphics[width=0.75\textwidth]{images/effbelle.png}
\end{center}
}
\only<3>{
\begin{center}
\includegraphics[width=0.75\textwidth]{images/jpsi.png}
\end{center}
}
\ARROW In Flavour physics we have ways to ensure we control our detector effects.


\end{footnotesize}
\end{minipage}

\end{frame}


\begin{frame}\frametitle{Published data format}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}

\ARROW There are number of ways the B-factories publish their results.\\
\ARROW Most of the time the information to links are on the collaboration web pages:\\


\begin{columns}
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/bellepub.png}
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/lhcbpub.png}


\end{columns}
\href{http://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/Summary_all.html}{\url{http://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/Summary_all.html}}\\

\href{http://belle.kek.jp/belle/publications.html}{\url{http://belle.kek.jp/belle/publications.html}}\\

\href{http://www.slac.stanford.edu/BFROOT/www/pubs/babarpubs.html}
{\url{http://belle.kek.jp/belle/publications.html}} 


\end{footnotesize}
\end{minipage}

\end{frame}

\begin{frame}\frametitle{CERN document server}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}
\only<1>{
\begin{center}
\includegraphics[width=0.95\textwidth]{images/cds.png}
\end{center}
}
\only<2>{
\begin{center}
\includegraphics[width=0.95\textwidth]{images/cds2.png}
\end{center}
}
\ARROW Figure on \texttt{CDS} and \texttt{LHCb publications page} available in many formats: \texttt{.pdf}, \texttt{.eps}, \texttt{.png}, \texttt{ROOT\_.C}\\
\ARROW No need to read the numbers from the plot any more!\\
\ARROW Supplementary material not included in the paper\\
(usually material that did not fit paper due to space constraints)
\end{footnotesize}
\end{minipage}

\end{frame}



\begin{frame}\frametitle{Unification of format}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}
\ARROW More and more results are being published on HepData make them ''one click away'' to get.
\begin{center}
\includegraphics[width=0.95\textwidth]{images/hepdata.png}
\end{center}

\end{footnotesize}
\end{minipage}

\end{frame}

\begin{frame}\frametitle{Unification of format}
{~}\\
	\begin{minipage}{\textwidth}
\ARROW More and more papers from Flavour community are appearing on \texttt{HepData}.\\
\begin{columns}
\column{0.05\textwidth}
{~}\\
\column{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/babar.png}
\column{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/belle.png}
\column{0.30\textwidth}
\includegraphics[width=0.95\textwidth]{images/lhcb.png}
\column{0.05\textwidth}
{~}\\
\end{columns}

\end{minipage}

\end{frame}





\begin{frame}\frametitle{This is not the end of the story!!}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}
\ARROW Even if experimentalist publish a number there is always a chance that the data might be misinterpreted by theorists.\\
\pause
\ARROW Many times the error gets symmetrized, the correlation neglected, or worse...\\
\begin{exampleblock}{Publish likelihood?}
\ARROWR The proposal that I would like to make for discussion is that HepData portal (or similar) would have a possibility that experiments could publish the whole multidim. likelihood function.\\
\ARROWR In this way we ensure that the function will be used as the experiment intended to.
\end{exampleblock}


\end{footnotesize}
\end{minipage}

\end{frame}
\iffalse


\begin{frame}{Global analysis}
{~}
	\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}{Analysis of Rare decays}
\begin{footnotesize}

%{\Large Since a long time ago...} \\ \medskip 
%\hspace*{1.4cm}$\Rightarrow$ $b \to s \gamma$ and $b \to s \ell\ell $ {\bf Flavour Changing Neutral Currents} have been used as {\bf \cred Our  Portal} \\ to explore the fundamental theory beyond SM. \\ 
%\medskip
%\medskip
%\hfill....... with not much success till 2013.\hspace*{1cm}
%\bigskip

Analysis of FCNC in a model-independent approach, effective Hamiltonian:
\vspace*{-0.1cm}
\begin{columns}
\begin{column}{1cm}
{~}
\end{column}
\begin{column}{8cm}
\begin{equation*}
b\to s\gamma(^*): {\mathcal H}^{SM}_{\Delta F=1} \propto  \sum_{i=1}^{10} V_{ts}^* V_{tb} {\cgreen C_i} \alert{  {\cal O}_i} + \ldots
\end{equation*}

\vspace{-0.2cm}

\begin{itemize}
\item $\alert{ {\cal O}_7} = \frac{e}{16 \pi^2}m_b\, (\bar s\sigma^{\mu\nu} P_R b) F_{\mu\nu}\,$ %\quad [real or soft photon]
\item $\alert{ {\cal O}_9}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b) (\bar\ell\gamma_\mu\ell)$
 %\quad [$b\to s\mu\mu$ via $Z$/hard $\gamma$]
\item $\alert{ {\cal O}_{10}}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b) (\bar\ell\gamma_\mu\gamma_5\ell)$, ...
%\quad [$b\to s\mu\mu$ via $Z$]
\end{itemize}
\end{column}
\begin{column}{5.5cm}
\includegraphics[width=3.5cm]{images/qum1.png} 
%\includegraphics[width=3cm]{bsll.pdf}
\end{column}
\end{columns}

%\hspace*{5cm} with no clear success yet...
%\bigskip


%\centerline{{\bf Goal}: \underline{Decode the short distance physics to find a smoking gun of BSM}\hspace*{2cm}}


\bigskip
\hspace*{0.0cm} $\bullet$ {\bf SM} Wilson coefficients up to NNLO + e.m. corrections at $\mu_{ref}=4.8$ GeV [{\cgreen Misiak et al.}]: $${\cal C}_7^{\rm SM}=-0.29,\, {\cal C}_9^{\rm SM}=4.1,\, {\cal C}_{10}^{\rm SM}=-4.3$$
%BUT, like in the film there is always the good, the bad and the ugly.
\bigskip
$\bullet$ {\bf NP} changes short distance ${\cal C}_i-{\cal C}_i^{\rm SM}={\cal C}_i^{\rm NP}$ and induce new operators, like ${\cal O}^\prime_{7,9,10}={\cal O}_{7,9,10}\,\, (P_L \leftrightarrow P_R)$ ... also scalars, pseudoescalar, tensor operators...%\bigskip

\begin{exampleblock}{Product placement}
There are many groups doing this kind of Willson Coefficients fits: \href{https://arxiv.org/abs/1510.04239}{1510.04239},  etc.
\end{exampleblock}

\end{footnotesize}

\end{frame}


\fi

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% GAMBIT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\begin{center}
\begin{Huge}
Global fits
\end{Huge}
\end{center}

\end{frame}


\begin{frame}                                                                                                                                                                                                                                
\frametitle{\textbf{GAMBIT}: a \textit{second-generation} global fit code}                                                                                                                                                                   
                                                                                                                                                                                                                                             
GAMBIT: The \alert{G}lobal \alert{A}nd \alert{M}odular \alert{B}SM \alert{I}nference \alert{T}ool                                                                                                                                            
\vspace{5mm}                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                             
Overriding principles of GAMBIT: flexibility and modularity                                                                                                                                                                                  
\begin{itemize}                                                                                                                                                                                                                              
\item General enough to allow fast definition of new datasets and theoretical models                                                                                                                                                         
\item Plug and play scanning, physics and likelihood packages                                                                                                                                                                                
\item Extensive model database -- not just small modifications to constrained MSSM (NUHM, etc), and not just SUSY!                                                                                                                           
\item Extensive observable/data libraries (likelihood modules)                                                                                                                                                                               
\item Many statistical options -- Bayesian/frequentist, likelihood definitions, scanning algorithms                                                                                                                                          
\item A smart and \textit{fast} LHC likelihood calculator                                                                                                                                                                                    
\item Massively parallel                                                                                                                                                                                                                     
\item Full open-source code release soon!                                                                                                                                                                                                          
\item Hear more in Anders Kvellestad tmr!
\end{itemize}                                                                                                                                                                                                                                
                                                                                                                                                                                                                                             
\end{frame}        

\begin{frame}                                                                                                                                                                                                                                
\frametitle{The GAMBIT Collaboration}                                                                                                                                                                                                        
                                                                                                                                                                                                                                             
\begin{columns}                                                                                                                                                                                                                              
\column{0.7\textwidth}                                                                                                                                                                                                                       
30 Members, 16 institutions, 10 countries,                                                                                                                                                                                                   
11 Experiments, 4 major theory codes\\ \vspace{2mm}                                                                                                                                                                                          
\scriptsize                                                                                                                                                                                                                                  
\begin{tabular}{l l}                                                                                                                                                                                                                         
\textbf{ATLAS} &  A.\ Buckley, C.\ Rogan,\\                                                                                                                                                                                     
               & M.\ White, \vspace{0.5mm}\\                                                                                                                                                                                                 
\textbf{Flavour exp.} & F.\ Bernlochner, M.\ Chrzaszcz, P.\ Jackson, N.\ Serra\vspace{0.5mm}\\                                                                                                                                                                                
\textbf{Fermi-LAT} &  J.\ Conrad, J.\ Edsj\"o, G.\ Martinez\\                                                                                                                                                                                
                   & P.\ Scott\vspace{0.5mm}\\                                                                                                                                                                                               
\textbf{CTA} &  C. Bal\'azs, T.\ Bringmann, \\                                                                                                                                                                                               
             & J.\ Conrad, M.\ White\vspace{0.5mm}\\                                                                                                                                                                                         
\textbf{HESS} &  J.\ Conrad \vspace{0.5mm}\\                                                                                                                                                                                                 
\textbf{IceCube} &  J.\ Edsj\"o, P.\ Scott\vspace{0.5mm}\\                                                                                                                                                                                   
\textbf{AMS-02} &  A.\ Putze\vspace{0.5mm}\\                                                                                                                                                                                                 
\textbf{CDMS, DM-ICE} &  L. Hsu\vspace{0.5mm}\\                                                                                                                                                                                              
\textbf{XENON/DARWIN} &  J.\ Conrad\vspace{0.5mm}\\                                                                                                                                                                                          
\textbf{Theory} &  P.\ Athron, C. Bal\'azs, T.\ Bringmann, \\                                                                                                                                                                                
                & J.\ Cornell, L.\ Dal, J.\ Edsj\"o, B.\ Farmer,\\                                                                                                                                                                           
                & A.\ Krislock, A.\ Kvellestad, M.\ Pato, \\                                                                                                                                                                                 
                & F.\ Mahmoudi, A.\ Raklev, P.\ Scott,\\                                                                                                                                                                                     
                & C.\ Weniger, M.\ White \\                                                                                                                                                                                                  
\end{tabular}\vspace{2mm}                                                                                                                                                                                                                    
                                                                                                                                                                                                                                             
{+recently joined: T. Gonzales, J. McKay, R. Ruiz, R. Trotta}\\                                                                                                                                                                        
{-recently retired: A.\ Saavedra, C.\ Savage}                                                                                                                                                                                          
\column{0.4\textwidth}                                                                                                                                                                                                                       
  \vspace{-15mm}                                                                                                                                                                                                                             
  \includegraphics[width=\linewidth]{Logo2full}\\\vspace{3mm}                                                                                                                                                                                
  \includegraphics[width=\linewidth]{GroupPhoto}                                                                                                                                                                                             
\end{columns}                                                                                                                                                                                                                                
                                                                                                                                                                                                                                             
\end{frame} 



\begin{frame}\frametitle{Global Analysis with Gambit}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}

\begin{columns} 
\begin{column}[c]{11.4cm} 

\begin{itemize}
 \item Wilson coefficients and $b \to s \ell^+ \ell^-$ observables implemented in {\bf\color{brique}SuperIso}\\[0.4cm]
 \item {\bf\color{brique}SuperIso}: public code for calculating flavour physics observables
{\hspace*{3.cm}\tiny \bf \color{vert}Mahmoudi, CPC 178 (2008) 745; CPC 180 (2009) 1579, CPC 180 (2009) 1718}\\[-0.1cm]
{\hspace*{3.cm}\tiny \bf \color{vert} available from http://superiso.in2p3.fr/}\\[0.4cm]
 \item {\bf\color{brique}SuperIso} interfaced into {\bf\color{brique}GAMBIT} through the flavour physics module {\bf\color{brique}FlavBit}\\[0.2cm]

{\hspace*{3.cm}\tiny \bf \color{vert}Web page: http://gambit.hepforge.org/}\\[0.4cm]
 \item {\bf\color{brique}FlavBit} determines the likelihoods by comparing the theoretical evaluations and the experimental results taking into account the experimental and theoretical correlations.  

\item In this study we used:
\begin{itemize}
\item $\PB \to \PKstar \Pmu \Pmu$ with all the $q^2$ bins and correlations matrices from HepData!
\item $\PB _{s/d} \to \Pmu \Pmu$
\item $\Pbeauty \to \Pstrange \gamma$
\end{itemize}


\end{itemize}

\end{column}
\end{columns}

\end{footnotesize}
\end{minipage}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\iffalse
\begin{frame}\frametitle{Global Analysis with Gambit - Results}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}



\end{footnotesize}
\end{minipage}

\end{frame}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}\frametitle{Global Analysis with Gambit - Results}
{~}\\
	\begin{minipage}{\textwidth}
\begin{footnotesize}

\begin{columns} 
\begin{column}[c]{5.2cm} 
\includegraphics[width=0.85\textwidth]{{plots/plot_WC_1_like1D_WC_MN}.pdf}\\
\includegraphics[width=0.85\textwidth]{{plots/plot_WC_2_like1D_WC_MN}.pdf}
\end{column}

\begin{column}[c]{6.0cm} 
\includegraphics[angle=-90,width=0.45\textwidth]{images/AFBPad.pdf}
\includegraphics[angle=-90,width=0.45\textwidth]{images/P5pPadOverlay.pdf}\\
\includegraphics[width=0.9\textwidth]{{plots/plot_WC_2_3_like2D_WC_MN}.pdf}\\
\ARROW Tension if $\Delta C_9$ observed!\\
\ARROW Other coefficients within SM predictions.\\
\ARROW $C_{10}$ still has a big uncertainty.

\end{column}


\end{columns}

\end{footnotesize}
\end{minipage}

\end{frame}


\begin{frame}\frametitle{Conclusions}
{~}\\
	\begin{minipage}{\textwidth}

\ARROW Flavour physics is a powerful tool to constrain NP models!\\
\ARROW Measurements are becoming more complex!\\
\ARROW Ability  to publish the full multidim. likelihoods soon will be needed!\\
\ARROW \textbf{GAMBIT} is the new player for fitting Flavour observables and will be made public soon.\\
\ARROW $3-4~\sigma$ deviations are present and Run2 data should clear the picture where it's NP or not.

\end{minipage}



\end{frame}





\backupbegin

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

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\frame { \frametitle{Numerical approach}



}




\backupend

\end{document}
