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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich, IFJ PAN)}
\institute{UZH, IFJ PAN}
\title[Overview of recent experimental results in flavour physics]{Overview of recent experimental results in flavour physics}
\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}{0.75\textwidth}
\flushright\fontspec{Trebuchet MS}\bfseries \LARGE {Overview of recent experimental results in flavour physics}
\end{column}
\begin{column}{0.02\textwidth}
{~}
\end{column}
\begin{column}{0.23\textwidth}
% \hspace*{-1.cm}
\vspace*{-3mm}
\includegraphics[width=0.6\textwidth]{lhcb-logo}
\end{column}
\end{columns}
\end{center}
\quad
\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
\end{column}
\begin{column}{0.53\textwidth}
\includegraphics[height=1.3cm]{uzh-transp}{~}{~}
\includegraphics[height=1.1cm]{ifj.png}
\end{column}
\end{columns}
\vspace{1em}
\footnotesize\textcolor{gray}{on behalf of the LHCb collaboration,\\ Universit\"{a}t Z\"{u}rich, \\ Institute of Nuclear Physics, Polish Academy of Science}\normalsize\\
\vspace{0.5em}
\textcolor{normal text.fg!50!Comment}{Pittsburgh, 3-6 May 2016}
\end{center}
\end{frame}
}
\begin{frame}{Flavour Physics, WHAT, WHY HOW?}
\begin{minipage}{\textwidth}
\begin{footnotesize}
{~}\\
\ARROW WHAT: Quarks and leptons exists in 6 ''flavours'' (u,c,t,d,s,b) and (e,$\mu$, $\tau$, $\nu_e$, $\nu_{\mu}$, $\nu_{\tau}$).\\
\ARROW WHY:
\begin{itemize}
\item Flavour is the heart of SM. It involves $22$ from $28$ free parameters, like masses mixing and CP violation.
\item Flavour physics loop processes (box and penguins) are sensitive to energy scales well beyond the ones of the accelerators, thanks to virtual contributions.
\end{itemize}
\begin{center}
\includegraphics[width=0.8\textwidth]{images/mglass.png}
\end{center}
\ARROW HOW:
\begin{itemize}
\item Compare precise theoretical predictions with precise experimental measurements.
\item LHCb, Belle, BaBar, ATLAS, CMS, NA62, BESIII, neutrinos experiments,...
\end{itemize}
\end{footnotesize}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}{Introduction to flavour physics}
\begin{minipage}{\textwidth}
\begin{footnotesize}
{~}\\{~}\\
\ARROW Masses and mixing of quarks have a common origin in the SM: The Yukawa interactions with the Higgs:
\begin{align*}
\mathcal{L}_{ \rm Yukawa}= - Y_{ij}^d \bar{Q^{\prime}}_{Li} \phi d^{\prime}_{Rj} - Y_{ij}^u \bar{Q^{\prime}}_{Ri} \phi u^{\prime}_{Rj}
\end{align*}
\ARROW The masses are generated using SSB by diagonalizing $Y$. The CKM matrix relats the mass eigenstates with the flavour eigenstates:
\begin{align*}
\begin{pmatrix}
d \\
s \\
b
\end{pmatrix}^{\prime}
=
\begin{pmatrix}
V_{ud} & V_{us} & V_{ub} \\
V_{cd} & V_{cs} & V_{cb} \\
V_{td} & V_{ts} & V_{tb}
\end{pmatrix}
\begin{pmatrix}
d \\
s \\
b
\end{pmatrix}^{ \rm phys}
\end{align*}
\ARROW The charge current interactions between quarks are proportional to the CKM matrix elements:
\begin{columns}
\column{3in}
\begin{align*}
\mathcal{L}_{CC}=-\frac{g}{\sqrt{2}} \bar{u} \gamma^{\mu}(1-\gamma^5)V_{CKM}d+...
\end{align*}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/in_thi9.png}
\end{columns}
\end{footnotesize}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}{CP violation}
\begin{minipage}{\textwidth}
\begin{footnotesize}
{~}\\{~}\\
\ARROW The $3 \times 3$ CKM has build inside the CP violation:
\begin{align*}
V_{ij} \neq V_{ij}^{\ast}~~\Rightarrow~~(CP)\mathcal{L}_{CC} \neq \mathcal{L}^{\dag}
\end{align*}
\ARROW In the Wolfenstein parametrization the CKM matrix reads:
\begin{align*}
V_{CKM}=
\begin{pmatrix}
1-\lambda^2/2 & \lambda & A\lambda^3({\color{red}\rho- i \eta})\\
-\lambda & 1-\lambda^2/2 & A \lambda^2 \\
A \lambda^3 ({\color{red}1-\rho - i \eta}) & -A \lambda^2 & 1
\end{pmatrix}
\end{align*}
\ARROW Strong hierarchy:
\begin{columns}
\column{2in}
\includegraphics[width=0.9\textwidth]{images/ckm.jpg}
\column{3in}
\includegraphics[width=0.9\textwidth]{images/quarkmasses.png}
\end{columns}
\end{footnotesize}
\end{minipage}
\vspace*{2.cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Why rare decays?}
\begin{columns}
\column{4in}
\begin{itemize}
\item In SM allows only the charged interactions to change flavour.
\begin{itemize}
\item Other interactions are flavour conserving.
\end{itemize}
\item One can escape this constrain and produce $\Pbottom \to \Pstrange$ and $\Pbottom \to \Pdown$ at loop level.
\begin{itemize}
\item This kind of processes are suppressed in SM $\to$~Rare decays.
\item New Physics can enter in the loops.
\end{itemize}
\end{itemize}
\begin{center}
\includegraphics[scale=0.3]{images/lupa.png}
\includegraphics[scale=0.3]{images/example.png}
\end{center}
\column{1.5in}
\includegraphics[width=0.61\textwidth]{images/couplings.png}
\end{columns}
\end{frame}
\begin{frame}{Searching for New Physics}
\begin{minipage}{\textwidth}
\begin{footnotesize}
{~}\\{~}\\
\ARROW The fundamental questions:
\begin{itemize}
\item Why 3 generations? Why such hierarchy structure?
\item Stability of the Higgs vacum? Dark Matter?
\item Baryon asymmetry of the universe? CP in SM is to small!
\end{itemize}
\pause
\ARROW Two ways to answer them:
\begin{itemize}
\item Direct searches: try to produce directly new real particles ''on-shell'', but we don’t
know their mass or lifetime and we are limited by the center-of-mass energy of
accelerator.
\item Indirect searches: study the effect of “off-shell” (virtual) particles within quantum
loop. Compare precise theoretical predictions with precise experimental measurements. Not limited by the center-of-mass energy of accelerator. It happened in the past:
\begin{itemize}
\item CP violation in the Kaon system: existence of $\Pbeauty$ and $\Ptop$ quarks.
\item Lack of observation of $\PKs \to \mu \mu$: existence of $\Pcharm$ quark.
\item Neutral weak currents: existence of $\PZ$ boson.
\end{itemize}
\item Very powerful tool!
\end{itemize}
\end{footnotesize}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}{Selected physics results:}
\begin{minipage}{\textwidth}
\begin{footnotesize}
{~}\\{~}\\
\begin{itemize}
\item Rare Decays
\begin{itemize}
\item $\PBs/ \PBd \to \Pmu \Pmu$
\item $\PBd \to \PKstar \Pmu \Pmu$, $\PBs \to \Pphi \Pmu \Pmu$, $\PLambdab \to \PLambda \Pmu \Pmu$.
\end{itemize}
\item Tests of lepton universalities:
\begin{itemize}
\item $R_k=\mathcal{B}(\PBplus \to \PKplus \Pmu \Pmu) / \mathcal{B}(\PBplus \to \PKplus \Pe \Pe)$
\item $R(\PD),~ R(\PDstar)$
\end{itemize}
\item $(g-2)_{\mu}$
\item CP violation:
\begin{itemize}
\item $\gamma$ angle
\item CP violation in $\PBd $ and $\PBs$
\item CP violation in charm
\item CP violation in kaons
\item $V_{ub}$
\end{itemize}
\item Tetra\&Pentaquarks
\end{itemize}
\end{footnotesize}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}
\begin{center}
\begin{Huge}
Rare decays
\end{Huge}
\end{center}
\end{frame}
\begin{frame}\frametitle{Tools}
\begin{itemize}
\item \textbf{Operator Product Expansion and Effective Field Theory}
\end{itemize}
\begin{columns}
\column{0.1in}{~}
\column{1.2in}
\begin{small}
\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{small}
\column{1.8in}
\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{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\PB_{d,s} \rightarrow \Pmu^+ \Pmu^-$}
\begin{columns}
\column{3.2in}
\begin{itemize}
\item Clean theoretical prediction, GIM and helicity suppressed in the SM:
\begin{itemize}
\item $\mathcal{B}(\PBs \to \Pmuon \APmuon) = (3.65 \pm 0.23)\times 10^{-9}$
\item $\mathcal{B}(\PBzero \to \Pmuon \APmuon) = (1.06 \pm 0.09)\times 10^{-10}$
\end{itemize}
\item Sensitive to contributions from scalar and pesudoscalar couplings.
\item Probing: MSSM, higgs sector, etc.
\item In MSSM: $\mathcal{B}(\PBs \to \Pmuon \APmuon) \sim \tan^6 \beta /m_A^4$
\item Theory errors dominated by the form factors! Will go down in the future.
\end{itemize}
\column{1.5in}
{~}
\includegraphics[width=0.95\textwidth]{hql/bs2mumu1.png}\\
\includegraphics[width=0.95\textwidth]{hql/bs2mumu2.png}\\
\includegraphics[width=0.6\textwidth]{hql/higgspen.png}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\PBzero \rightarrow \Pmu^+ \Pmu^-$ Results}
\begin{columns}
\column{2.in}
\begin{itemize}
\item Nov. 2012:
\begin{itemize}
\item First evidence $3.5\sigma$ for $B^0 \rightarrow \mu^+ \mu^-$. with $2.1~\rm fb^{-1}$.
\end{itemize}
\item Summer 2013:
\begin{itemize}
\item Full data sample: $3~\rm fb^{-1}$.
\end{itemize}
\end{itemize}
\column{3.0in}
\includegraphics[width=0.95\textwidth]{hql/mass2.png}
\end{columns}
\begin{itemize}
\item Measured BF:\\ $\mathcal{B}(\PBs \to \Pmuon \APmuon) =(2.9^{+1.1}_{-1.0}(stat.)^{+0.3}_{-0.1}(syst.))\times 10^{-9}$
\item $4.0 \sigma$ significance!
\item $\mathcal{B}(\PBzero \to \Pmuon \APmuon) < 7 \times 10^{-10}$ at $95\%$ CL
%\item \href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110.021801}{\color{blue} PRL 110 (2013) 021801 }
\item \href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.101805}{\color{blue} CMS result: PRL 111 (2013) 101805}
\end{itemize}
\textref{ PRL 110 (2013) 021801}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{LHCb+CMS Combination}
\begin{columns}
\column{3in}
\begin{large}
\begin{center}
$\mathcal{B}(\PBs \to \Pmuon \APmuon) =(2.8^{+0.7}_{-0.6} )\times 10^{-9}$\\
$\mathcal{B}(\PBzero \to \Pmuon \APmuon) =(3.9^{+1.6}_{-1.4} )\times 10^{-10}$
\end{center}
\end{large}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/nature.png}
\end{columns}
\includegraphics[width=0.95\textwidth]{hql/bs2mumu_comb.png}
\ARROW $2.3~\sigma$ compatibility with SM!
\textref{Nature 522 (2015) 68}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{ATLAS enters the game}
\begin{columns}
\column{3in}
\begin{itemize}
\item $\mathcal{B}(\PBs \to \Pmuon \APmuon) =0.9^{+1.1}_{-0.8} \times 10^{-9}$\\
\item $\mathcal{B}(\PBzero \to \Pmuon \APmuon) <4.2 \times 10^{-10} $ at $95~\rm CL$
\end{itemize}
\includegraphics[width=0.95\textwidth]{images/atlas2.png}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/atlas.png}\\
\includegraphics[width=0.95\textwidth]{images/atlas3.png}
\end{columns}
\textref{arXiv:1604.04263}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBd \to \PKstar \Pmu \Pmu$}
\begin{footnotesize}
{~}\\
\begin{minipage}{\textwidth}
\ARROW The decay of $\PBd \to \PKstar \Pmu \Pmu$ has number of angular observables that are sensitive to different Wilson coefficients: $C_7^{(\prime)},~C_9^{(\prime)},~C_{10}^{(\prime)}$.\\
\ARROW The complete angular expression is given by:
\iffalse
{\tiny{
\begin{align*}
\label{dist}
\dfrac{1}{d \Gamma /dq^2} \frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi} = \frac9{32\pi}[ \frac{3}{4}(1- {\color{red}{F_L}} \sin^2\theta_K + {\color{red}{F_L}} \cos^2\theta_K + \\ \frac{1}{4} (1-{\color{red}{F_L }} )\sin^2\theta_K \cos 2\theta_l \\ - {\color{red}{F_L}} \cos^2\theta_K \cos 2\theta_l + {\color{red}{S_3}} \sin^2\theta_K \sin^2\theta_l \cos 2\phi + {\color{red}{S_4}} \sin 2\theta_K \sin 2\theta_l \cos\phi + {\color{red}{S_5}} \sin 2\theta_K \sin\theta_l \cos\phi \\ + ({\color{red}{S_{6s}}} \sin^2\theta_K + {\color{red}{{S_{6c}}}} \cos^2\theta_K) \cos\theta_l + {\color{red}{S_7}} \sin 2\theta_K \sin\theta_l \sin\phi + {\color{red}{S_8}} \sin 2\theta_K \sin 2\theta_l \sin\phi + {\color{red}{S_9}} \sin^2\theta_K \sin^2\theta_l \sin 2\phi ]
\end{align*}
}}
\fi
\begin{center}
\includegraphics[width=0.85\textwidth]{images/angles4.png}
\end{center}
\ARROW Furthermore, one can construct a form factor free observables:
\begin{align*}
P_5^{\prime}=\frac{S_5}{F_L(1-F_L)}
\end{align*}
\end{minipage}
\vspace*{2.1cm}
\vspace*{2.1cm}
\end{footnotesize}
\textref{JHEP, 1305:137, (2013)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBd \to \PKstar \Pmu \Pmu$ results}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.65\textwidth]{images/p5pbelle.png}\\
\end{center}
\begin{itemize}
\item Tension with $3~\invfb$ gets confirmed!
\item Two bins both deviate by $2.8~\sigma$ from SM prediction.
\item Result compatible with previous results and Belle!
\item SM: \href{http://arxiv.org/abs/1407.8526}{\color{blue}JHEP12(2014)125}
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\textref{arxiv:1604.04042}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBd \to \PKstar \Pmu \Pmu$ results}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\only<3>
{
\ARROW Method of Moments allowed us to measure for the first time a new observable:
}
\begin{center}
\only<1>{
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_FLPad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S3Pad.pdf}\\
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S4Pad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S5Pad.pdf}
}
\only<2>{
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_AFBPad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S7Pad.pdf}\\
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S8Pad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S9Pad.pdf}\\
\ARROW $S_7$, $S_8$, $S_9$ are zero in the SM!
}
\only<3>{
\includegraphics[angle=-90,width=0.75\textwidth]{images/S6cPad.pdf}\\
\begin{flushleft}
\ARROW LHCb also measured the CP asymmetries with Method of Moments and the likelihood fit that are consistent with SM
\end{flushleft}
}
\end{center}
\end{minipage}
\end{footnotesize}
\textref{JHEP 02 (2016) 104}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Compatibility with SM}
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{0.1in}
{~}
\column{2in}
\ARROW Use \texttt{EOS} software package to test compatibility with SM.\\
\ARROW Perform the $\chi^2$ fit to the measured:
\begin{center}
\begin{align*}
F_L, A_{FB}, S_{3,..., 9} .
\end{align*}
\end{center}
\ARROW Float a vector coupling: $\Re(C_9)$.\\
\ARROW Best fit is found to be $3.4~\sigma$ away from the SM.
\column{3in}
\begin{align*}
\Delta \Re (C_9) \equiv \Re(C_9)^{{\rm fit}} - \Re(C_9)^{{\rm SM}} = -1.03
\end{align*}
\includegraphics[angle=-90,width=0.95\textwidth]{images/wilsonchi2.pdf}
\end{columns}
\end{minipage}
\textref{JHEP 02 (2016) 104}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{BF 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 than SM prediction.
\end{itemize}
\column{0.6\textwidth}
\includegraphics[width=0.87\textwidth]{images/bukst_BF.png}
\end{columns}
\end{center}
\textref{JHEP 07 (2012) 133}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{BF of $\PBs \to \Pphi \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.65\textwidth]{images/bs2phipi.png}\\
\end{center}
\begin{itemize}
\item Last years LHCb measurement. %\href{http://arxiv.org/abs/1506.08777}{{\color{blue}{JHEP09 (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}
\textref{JHEP09 (2015) 179}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{BF 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=0.55\textwidth]{images/Lblow.png}
\includegraphics[width=0.55\textwidth]{images/Lbhigh.png}
}
\end{center}
\begin{itemize}
\item Last years LHCb measurement.% [{\color{blue}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}
\textref{JHEP 06 (2015) 115}
\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}
\textref{JHEP 06 (2015) 115}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Lepton Universlaity tests
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\begin{Huge}
Lepton Universality tests
\end{Huge}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Lepton universality test}
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{3.0in}
\begin{itemize}
\item Does the NP couple equally to all flavours?
\includegraphics[width=0.99\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}\\
\includegraphics[width=0.95\textwidth]{images/diagramsRK.png}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\textref{Phys. Rev. Lett. 113, 151601 (2014)}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{More Lepton universality tests}
{~}
\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: $R(\PDstar)= 0.336 \pm 0.027 \pm 0.030$
\item HFAG average: $R(\PDstar)=0.322 \pm 0.022$
\item $4.0~\sigma$ discrepancy wrt. SM.
\end{itemize}
\begin{center}
\includegraphics[width=0.48\textwidth]{images/RDstar.png}
\end{center}
%\textref{http://www.slac.stanford.edu/xorg/hfag/index.html}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Explanation of anomalies}
{~}
\begin{minipage}{\textwidth}
\ARROW Thanks to S. Descotes-Genon, L.Hofer, J.Matias, J.Virto we have a global fit to the anomalies.\\
\begin{center}
\includegraphics[width=0.75\textwidth]{images/quim2.png}
\end{center}
\ARROW The fit prefer a modification of $C_9$ Wilson coefficient with a value of $C_9^{NP}=-1$, with a significance over $4\sigma$.\\
%\ARROW Many theories link might accommodate the observed deviations.
\textref{arXiv:1510.04239}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Explanation of anomalies}
{~}
\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}
\includegraphics[width=0.9\textwidth]{images/charmloop.png}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{}
\begin{center}
\begin{Huge}
$(g-2)_{\mu}$
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Muon anomalous magnetic moment $(g-2)_{\mu}$}
{~}
\begin{minipage}{\textwidth}
\ARROW Dirac equations predict a muon magnetic moment $\overrightarrow{M}=g_{\mu} \frac{e}{2m_{\mu}}\overrightarrow{S}$ with a gyromagnetic ratio $g_{\mu}=2$. Experimentally $g_{\mu}>2$.\\
\ARROW This anomaly $a_{\mu}$ arises from calculable quantum fluctuations:
\begin{center}
\includegraphics[width=0.8\textwidth]{images/gm2.png}
\end{center}
\ARROW SM value $a_{\mu}^{\rm SM}=(116 591 803 \pm 49) \times 10^{-11}$ [PDG 2014]\\
\ARROW Experiment: $a_{\mu}^{\rm E821}=(116 592 091 \pm 63) \times 10^{-11}$ [PDG 2014]\\
\ARROW Difference: $a_{\mu}^{\rm E821} -a_{\mu}^{\rm SM} =(288 \pm 80)\times 10^{-11}$ $\Leftrightarrow$ $3.6~\sigma$!\\
\ARROW Underestimated uncertainties? SUSY? NP?\\
\ARROW Fermilabs E989 should futher reduce the experimental error\\ to $\pm16 \times 10^{-11}$.
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% CP violation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\gamma$ angle}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\ARROW $\gamma = \arg \left(- \frac{V_{ud}V_{ub}^{\ast} }{ V_{cd}V_{cb}^{\ast} }\right) \approx \arg(- \frac{V_{ub}^{\ast}}{V_{cb}^{\ast}})$ is the last well known CKM angles.\\
\ARROW Can be determined by:
\begin{itemize}
\item Tree level processes, nearly insensitive to NP. Act as reference. Negligible theoretical uncertainty, using $\PB \to \PD \PK$.
\item Loop processes, sensitive to NP.
\end{itemize}
\ARROW Comparing the two can reveal NP!
\begin{columns}
\column{2.2in}
\includegraphics[width=0.9\textwidth]{images/gamma.png}
\column{2.8in}
\ARROW The LHCb combinations leads to: $\gamma = {70.9^{+7.1}_{-8.5} }^{\circ} $.\\
\ARROW Improved by $2^{\circ}$ compared to our previous result!\\
\ARROW Other B-factories have 2 times larger errors:
\begin{itemize}
\item BaBar: $\gamma=(70\pm 18)^{\circ}$
\item Belle: $\gamma=(73^{+18}_{-15})^{\circ}$
\end{itemize}
\end{columns}
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Mixing induced CPV in $\PBs$}
{~}
\begin{small}
\begin{minipage}{\textwidth}
\ARROW Interference between $\PBs$ decaying to $\PJpsi \Pphi$ either directly or by oscillations gives rise to CP violation phase: $\phi_s^{\PJpsi \Pphi}$
\begin{center}
\includegraphics[width=0.85\textwidth]{images/phis.png}
\end{center}
\ARROW In the SM $\phi_s \approx -2 \beta_s = -(0.0376^{+0.0007}_{-0.0008})~\rm rad$, where $\beta_s=\arg \left(- \frac{V_{ts}V_{tb}^{\ast}}{V_{cs} V_{cb}^{\ast}} \right)$\\
\ARROW At the leading order same phase is expected $\PBs \to \PDs \PDs$ and $\PB \to \PJpsi \Ppi \Ppi$.\\
\ARROW NP can enter in the $\PBs$ mixing!\\
\ARROW Measured by simultaneous fit to $\PBs$ and $\bar{\PBs}$ decay rates:
\begin{center}
\includegraphics[width=0.9\textwidth]{images/phis2.png}
\end{center}
\end{minipage}
\end{small}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Mixing induced CPV in $\PBs$}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\ARROW Unbinned maximum likelihood fit (time, mass, angles, initial flavour):
\begin{center}
\includegraphics[width=0.6\textwidth]{images/Bsmix.png}
\end{center}
\begin{itemize}
\item $\phi_s=-0.058 \pm 0.049 \pm 0.006$ rad.
\item $\Gamma_s=(\Gamma_L+\Gamma_H)/2=0.6603\pm 0.0027 \pm 0.0015~ {\rm ps}^{-1}$
\item $\Delta \Gamma_s=\Gamma_L-\Gamma_H=0.0805 \pm 0.0091 \pm 0.0032~ {\rm ps}^{-1}$
\item Combined with $\PBs \to \PJpsi \pi \pi$: $\phi_s=-0.010 \pm 0.039$ rad.
\end{itemize}
\end{minipage}
\end{footnotesize}
\textref{PRL 114, 041801 (2015)}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Mixing induced CPV in $\PBs$}
{~}
\begin{footnotesize}
\begin{center}
\includegraphics[width=0.7\textwidth]{images/hfagccs.png}
\end{center}
\ARROW LHCb is dominating the world average!\\
\ARROW $\phi_s^{ \rm HFAG}=-0.034 \pm 0.033$.\\
\ARROW Compatible with SM, but there is still plenty room for NP!\\
\ARROW Penguin pollution constrained from $\PBzero \to \PJpsi \Prho$ and $\PBs \to \PJpsi \bar{\PKstar}$
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{$V_{ub}$}
{~}
\begin{footnotesize}
\ARROW Since a long time the smallest of the CKM matrix elements $V_{ub}$ has been determined in two ways:
\begin{itemize}
\item inclusively: $\Pbeauty \to \Pup \ell \nu$, $\vert V_{ub} \vert=(4.41 \pm 0.15^{+0.15}_{-0.17})\times 10^{-3}$
\item exclusively: $\PB \to \pi \ell \nu$, $\vert V_{ub} \vert=(3.28 \pm 0.29)\times 10^{-3}$
\item $3~\sigma$ tensions!
\end{itemize}
\ARROW LHCb perspectively enters the game with baryons decay: $\PLambdab \to \Pproton \mu \nu$.
\begin{center}
\includegraphics[width=0.45\textwidth]{images/vub.png}
\end{center}
where $R_{FF}$ is a ratio of form factors, that can be calculated using lattice QCD [arxiv:1503.01421].
\end{footnotesize}
\textref{Nature Physics 11, 743-747 (2015)}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{$V_{ub}$}
{~}
\begin{footnotesize}
\ARROW $\vert V_{ub}\vert = (3.27 \pm0.15 \pm 0.16 \pm 0.06(V_{cb})) \times 10^{-3}$
\begin{center}
\includegraphics[width=0.95\textwidth]{images/vub2.png}
\end{center}
\begin{itemize}
\item LHCbs measurement makes the discrepancy larger and is spot on the Exclusive B-factories results.
\item Disfavor NP models with significant right handed current
\item Debatable world averages, depending on the input used (theory, BR of control mode, ...)
\end{itemize}
\end{footnotesize}
\textref{Nature Physics 11, 743-747 (2015)}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{CP violation in charm}
{~}
\begin{footnotesize}
\ARROW The $A_{CP}$ asymmetry is defined as:
\begin{align*}
A_{CP}(\PDzero \to f) = \frac{\Gamma(\PDzero \to f)-\Gamma(\bar{\PDzero} \to f) }{\Gamma(\PDzero \to f)+\Gamma(\bar{\PDzero} \to f) },~~~f=\PK^+ \PK^- ,\Ppi^+ \Ppi^-
\end{align*}
\begin{center}
\includegraphics[width=0.65\textwidth]{images/charmCP.png}
\end{center}
\ARROW New world average:
\begin{align*}
a_{CP}^{ \rm ind}=(0.056 \pm 0.040)\% \\
a_{CP}^{ \rm dir}=(-0.137 \pm 0.070)\%
\end{align*}
\ARROW Results consistent with no CPV at $6.5~\%$ CL.
\end{footnotesize}
\textref{LHCb-PAPER-2015-055, PLB 753 (2016) 412}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Direct CPV in kaons}
{~}
\begin{small}
\ARROW 1999: Discovery of CP violation in $\PK \to \pi \pi$ (NA48, KTeV).\\
\ARROW 2001: Combined experimental average of the two above experiments: $\Re (\epsilon^{\prime}/ \epsilon )=(16.6\pm 2.3)\times 10^{-4}$, compatible with SM. Experimental precision much better than the theoretical prediction.\\
\ARROW 2015: Fantastic progresses in lattice QCD. Can now compute all relevant long-distance effects that used to dominate the theoretical uncertainty:
\begin{align*}
\Re (\epsilon^{\prime}/ \epsilon )=(1.9 \pm 4.5)\times 10^{-4}
\end{align*}
\ARROW A brand new $2.9~\sigma$ tension arrives!\\
\ARROW A.Buras, et.al. [JHEP03(2016)010] This discrepancy can be linked to aforementioned $\Pbeauty \to \Pstrange \ell \ell$ anomalies. \\
\ARROW Good lattice prospects to improve even further the theoretical uncertainty
\end{small}
\textref{A. Buras et al, arXiv:1507.06345}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Global CKM fit}
{~}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/CKMfit.png}
\end{center}
\ARROW Excellent consistency of the various CKM measurements so far!
\textref{\url{http://ckmfitter.in2p3.fr}}
\vspace*{2.1cm}
\end{frame}
\begin{frame}
\begin{center}
\begin{Huge}
Tetra\&Petraquarks
\end{Huge}
\end{center}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Tetra\&Petraquarks}
{~}
\ARROW Idea of this multi quark states started in the $1960$s:
\begin{center}
\includegraphics[width=0.7\textwidth]{images/gelman.png}
\end{center}
\ARROW Searches for years and many “discoveries” not confirmed
\vspace*{2.1cm}
\end{frame}
\iffalse
\begin{frame}{X(3872)}
{~}
\begin{footnotesize}
\begin{columns}
\column{0.1in}
{~}\\
\column{2.5in}
\ARROW First observed by Belle in $\PB^+ \to X(\PJpsi \pi \pi) \PK^+$, above the $\PUpsilon(2S)$. [PRL 91 (2003) 262001]\\
\ARROW Confirmed by several experiments: BaBar, CDF, D0, LHCb, CMS.\\
\ARROW LHCb determined its quantum numbers: $J^{PC}=1^{++}$ using angular analysis [PRL 110, 222001 (2013)].\\
{~}\\
\ARROW The nature of this state is still unclear. It is compatible with a tetraquark, $\PD\PDstar$ molecule or a $\chi_{c1}(2^3P_1)$ hypothesis.\\
\ARROW Never LHCb measurements disfavour the $\PD\PDstar$ molecule by $4.4~\sigma$ [Nucl. Phys. B886 (2014) 665].
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/x3872.png}
\end{columns}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\fi
\begin{frame}{$Z(4430)^-$}
{~}
\begin{footnotesize}
\begin{columns}
\column{0.1in}
{~}\\
\column{2.5in}
\ARROW $Z(4430)^-$ special “tetraquark candidate”,because charged: cannot be a $\Pcharm \bar{\Pcharm}$ state!\\
\ARROW Belle discovered it in $\PBzero \to \PUpsilon(2S)\PK \Ppi$, with evidence of $J^{P}=1^+$ [PRD 88 (2013) 074026]. \\
\ARROW Using method of moments, Babar claimed they do not need the $Z(4430)^-$ to described their data [PRD 79 (2009) 112001].\\
\ARROW LHCb reproduced BaBar moments analysis with the full Run1 sample ($3~\invfb$) and clearly something mote was needed to describe the data [PRL 112, 222002 (2014)].\\
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/Z4430.png}
\end{columns}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{$Z(4430)^-$}
{~}
\begin{footnotesize}
\ARROW LHCb unbinned amplitude analysis of $\PBzero \to \Ppsi(2S) \PK^+ \Ppi^-$, $m=4475 \pm 7 ^{+15}_{-25}~\MeV/c^2$, $\Gamma=172 \pm 13^{37}_{34}~\MeV/c^2$\\
\ARROW $J^P$ is confirmed to be $1^+$ and Argand plot shows the typical pattern for resonances.\\
\ARROW Minimal quark content $\Pcharm \APcharm \Pdown \APup$.
\begin{center}
\includegraphics[width=0.9\textwidth]{images/Z44301.png}
\end{center}
\end{footnotesize}
\textref{LHCb, PRL 112, 222002 (2014)}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Pentaquarks in $\PLambdab \to \PJpsi \Pproton \PK$}
{~}
\begin{footnotesize}
\ARROW $\PLambdab \to \PJpsi \Pproton \PK$ was studied initially for a precise $\PLambdab$ lifetime .\\
\ARROW Close look at the Dalitz: $m(\PK\Pproton)-m(\PJpsi \Pproton)$
\begin{itemize}
\item $m(\PK\Pproton)$ has a rich structure of excited $\PLambda$ states.
\item $m(\PJpsi \Pproton)$ has something inside!
\end{itemize}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/penta.png}
\end{center}
\end{footnotesize}
\textref{[LHCb, PRL 115 (2015) 072001]}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Pentaquarks in $\PLambdab \to \PJpsi \Pproton \PK$}
{~}
\begin{footnotesize}
\ARROW Super complex fit needed to describe the data: $5$ decay angles, $14$ possible $\PLambda^{\ast}$ resonances for $m(\PK \Ppi)$ and two brand new pentaquarks for $m(\PJpsi \Pproton)$:
\begin{itemize}
\item $P_c(4380)^+$: $4380\pm 8 \pm 29~\MeV/c^2$, $\Gamma=205 \pm 18 \pm 86~\MeV/c^2$, $J^P=\frac{3}{2}^-$
\item $P_c(4450)^+$: $4449,8\pm 1.7 \pm 2.5~\MeV/c^2$, $\Gamma=39 \pm 5 \pm 19~\MeV/c^2$, $J^P=\frac{5}{2}^+$
\end{itemize}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/penta2.png}
\end{center}
\end{footnotesize}
\textref{[LHCb, PRL 115 (2015) 072001]}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Pentaquarks in $\PLambdab \to \PJpsi \Pproton \PK$}
{~}
\begin{footnotesize}
\begin{columns}
\column{3in}
\begin{itemize}
\item Angrad plots show the phase motion for the resonances.
\item The $P_c(4380)$ has one point off by a $2\sigma$.
\end{itemize}
\column{2in}
\begin{itemize}
\item The interference patterns confirm the opposite parities.
\end{itemize}
\end{columns}
\begin{center}
\includegraphics[width=0.99\textwidth]{images/penta3.png}
\end{center}
\ARROW The significance was evaluated with a TOY MC:
\begin{itemize}
\item $P_c(4380)^+:~9\sigma$
\item $P_c(4450)^+:~12\sigma$
\end{itemize}
\ARROW The states are consistent with $\Pcharm \APcharm \Pup \Pup \Pdown$.\\
\end{footnotesize}
\textref{[LHCb, PRL 115 (2015) 072001]}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Conclusions}
{~}
\begin{small}
\ARROW Flavour physics is still playing an important role for hunting new physics!\\
\ARROW Anomalies in the electroweak penguin and lepton universality combine to over $4\sigma$ significance discrepancy for NP.\\
\ARROW The dominant anomaly was recently confirmed by Belle experiment.\\
\ARROW $\gamma$ angle combination from LHCb is now two times more precise then the B-factories.\\
\ARROW After $50$ years after the first Prof. Gelman paper the pentraquark states have been observed.\\
\ARROW Stay tuned as there are plenty of more results in the pipe line!
\end{small}
\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}
\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 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}{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}\nonumber}
}}
\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 (soft form factors):
{\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}\nonumber}
}}
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)} }\nonumber
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Mass modelling}
{~}
\begin{minipage}{\textwidth}
\begin{small}
\begin{columns}
\column{0.1in}
{~}
\column{2.5in}
\ARROW The signal is modelled by a sum of two Crystal-Ball functions with common mean.\\
\ARROW The background is a single exponential.\\
\ARROW The base parameters are obtained from the proxy channel: $\PBd \to \PJpsi (\mu\mu) \PKstar$.\\
\ARROW All the parameters are fixed in the signal pdf.\\
\ARROW Scaling factors for resolution are determined from MC.\\
\ARROW In fitting the rare mode only the signal, background yield and the slope of the exponential is left floating.\\
\ARROW We found $624\pm30$ candidates in the most interesting $\left[1.1,6.0\right]~\GeV^2/c^4$ region \\ and $2398 \pm 57$ in the full range $\left[ 1.1, 19.\right]~\GeV^2/c^4$.
\column{2.5in}
\begin{center}
\includegraphics[angle=-90,width=0.9\textwidth]{images/msignal.pdf}\\
\end{center}
\ARROW The S-wave fraction is extracted using a \texttt{LASS} model.
\end{columns}
\end{small}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\iffalse
%%%%%%%%%%%%%%%
\begin{frame}{Monte Carlo corrections}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\ARROW No Monte Carlo simulation is perfect! One needs to correct for remaining differences.\\
\ARROW We reweighted our $\PBd \to \PKstar \mu \mu$ Monte Carlo accordingly to differences between the $\PBd \to \PKstar \PJpsi$ in data (Splot) and Monte Carlo.
\only<1>{
\begin{center}
\includegraphics[angle=-90,width=0.38\textwidth]{images/pt.pdf}
\includegraphics[angle=-90,width=0.38\textwidth]{images/vertex.pdf}\\
\includegraphics[angle=-90,width=0.38\textwidth]{images/nTracks.pdf}
\end{center}
}
\only<2>{
\begin{center}
\includegraphics[angle=-90,width=0.38\textwidth]{images/eta_logy.pdf}
\includegraphics[angle=-90,width=0.38\textwidth]{images/B0_p.pdf} \\
\includegraphics[angle=-90,width=0.38\textwidth]{{images/bdt_data_mc_nominalMkpi}.pdf}
\end{center}
}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Detector acceptance}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\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 $\cos \thetal, \cos \thetak, \phi, q^2$.
\item The coefficients were determined using Method of Moments, with a huge simulation sample.
\item The simulation was done assuming a flat phase space and reweighing the $q^2$ distribution to make is flat.
\end{itemize}
%\includegraphics[width=0.75\textwidth]{images/q2PHSP.png}
\column{0.4\textwidth}
%\only<1>{
%\includegraphics[width=0.99\textwidth]{images/q2PHSP.png}\\
%\includegraphics[width=0.99\textwidth]{images/q2PHSPw.png}
%}
\only<1>{
\includegraphics[width=0.99\textwidth]{images/det.png}
}
\end{columns}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Control channel}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\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}
\end{footnotesize}
\begin{center}
\includegraphics[angle=-90,width=0.4\textwidth]{images/mlogjpsi.pdf}
\includegraphics[angle=-90,width=0.4\textwidth]{images/mkpijpsi.pdf}\\
\includegraphics[width=0.99\textwidth]{images/angles3.png}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The columns of New Physics}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.94\textwidth]{images/columns.png}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBd \to \PKstar \Pmu \Pmu$ results}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\ARROW In the maximum likelihood fit one could weight the events accordingly to the $\dfrac{1}{\varepsilon(\cos \thetal, \cos \thetak, \phi, q^2)}$\\
\ARROW Better alternative is to put the efficiency into the maximum likelihood fit itself:
\begin{align*}
\mathcal{L}=\prod_{i=1}^N \epsilon_i(\Omega_i, q_i^2) \mathcal{P}(\Omega_i, q_i^2) / \int \epsilon(\Omega, q^2) \mathcal{P}(\Omega, q^2) d\Omega dq^2
\end{align*}
\ARROW Only the relative weights matters!\\
\ARROW The Procedure was commissioned with TOY MC study.\\
\ARROW Use Feldmann-Cousins to determine the uncertainties. \\
\ARROW Angular background component is modelled with $2^{\rm nd }$ order Chebyshev polynomials, which was tested on the side-bands.\\
\ARROW S-wave component treated as nuisance parameter.\\
\includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_Afb3}.pdf}
\includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P11}.pdf}
\includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P57}.pdf}
\end{minipage}
\end{footnotesize}
\textref{JHEP 02 (2016) 104}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Maximum likelihood fit - Results}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\only<1>{
\includegraphics[angle=-90,width=0.45\textwidth]{images/FLPad.pdf}
\includegraphics[angle=-90,width=0.45\textwidth]{images/S3Pad.pdf}\\
\includegraphics[angle=-90,width=0.45\textwidth]{images/S4Pad.pdf}
\includegraphics[angle=-90,width=0.45\textwidth]{images/S5Pad.pdf}
}
\only<2>{
\includegraphics[angle=-90,width=0.45\textwidth]{images/AFBPad.pdf}
\includegraphics[angle=-90,width=0.45\textwidth]{images/S7Pad.pdf}\\
\includegraphics[angle=-90,width=0.45\textwidth]{images/S8Pad.pdf}
\includegraphics[angle=-90,width=0.45\textwidth]{images/S9Pad.pdf}
}
\end{center}
\ARROW SM: \href{http://arxiv.org/abs/1411.3161}{ {\color{blue}Eur.Phys.J. C75 (2015) no.8, 382 }}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Method of moments}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\ARROW See {\color{blue}{\href{http://arxiv.org/abs/1503.04100}{Phys.Rev.D91(2015)114012}}}, F.Beaujean , M.Chrzaszcz, N.Serra, D. van Dyk for details.\\
\ARROW The idea behind Method of Moments is simple: Use orthogonality of spherical harmonics, $f_j(\overrightarrow{\Omega})$ to solve for coefficients within a $q^2$ bin:
\begin{align*}
\int f_i(\overrightarrow{\Omega}) f_j(\overrightarrow{\Omega}) = \delta_{ij}
\end{align*}
\begin{align*}
M_i = \int \left( \dfrac{1}{d(\Gamma+ \bar{\Gamma})/dq^2} \right) \dfrac{d^3(\Gamma+\bar{\Gamma})}{d \overrightarrow{\Omega}} f_i(\overrightarrow{\Omega})d \Omega
\end{align*}
\ARROW Don’t have true angular distribution but we ''sample'' it with our data.\\
\ARROW Therefore: $\int \to \sum$ and $M_i \to \widehat{M}_i$
\begin{align*}
\hat{M}_i=\dfrac{1}{\sum_e \omega_e} \sum_e \omega_e f_i(\overrightarrow{\Omega}_e)
\end{align*}
\ARROW The weight $\omega$ accounts for the efficiency. Again the normalization of weights does not matter.
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Amplitudes method}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\ARROW Fit for amplitudes as (continuous) functions of $q^2$ in the region: $q^2 \in \left[ 1.1. 6.0 \right]~\GeV^2/c^4$.\\
\ARROW Needs some Ansatz:
\begin{align*}
A(q^2) = \alpha + \beta q^2+ \dfrac{\gamma}{q^2}
\end{align*}
\ARROW The assumption is tested extensively with toys.\\
\ARROW Set of 3 complex parameters $ \alpha, \beta, \gamma $ per vector amplitude:\begin{itemize}
\item {\color{Magenta}{$L, ~R$}}, {\color{Cerulean}{$0 ,~\| ,~\bot$}}, {\color{PineGreen}{$\Re ,~\Im$}} $\rightarrowtail$~~ $3 \times {\color{PineGreen}{2}} \times {\color{Cerulean}{3}} \times {\color{Magenta}{2}} = 36$ DoF.
\item Scalar amplitudes: $+4$ DoF.
\item Symmetries of the amplitudes reduces the total budget to: $28$.
\end{itemize}
\ARROW The technique is described in \href{http://arxiv.org/pdf/1504.00574v2.pdf}{\color{blue}{JHEP06(2015)084}}, U. Egede, M. Patel, K.A. Petridis.\\
\ARROW Allows to build the observables as continuous functions of $q^2$:
\begin{itemize}
\item At current point the method is limited by statistics.
\item In the future the power of this method will increase.
\end{itemize}
\ARROW Allows to measure the zero-crossing points for free and with smaller errors than previous methods.
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Amplitudes - results}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\begin{center}
\begin{columns}
\column{0.45\textwidth}
\includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_AFBOverlay}.pdf}\\
\includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S4Overlay}.pdf}
\column{0.45\textwidth}
\includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S5Overlay}.pdf}\\
{~}\\{~}\\{~}\\{~}\\
\begin{large}
Zero crossing points:
\end{large}
\begin{align*}
q_0(S_4) & <2.65 & {\rm{~at~}} & 95\% ~CL \\
q_0(S_5) & \in \left[ 2.49,3.95 \right] & {\rm{~at~}} & 68\% ~CL \\
q_0(A_{FB}) & \in \left[ 3.40, 4.87 \right] & {\rm{~at~}} & 68\% ~CL
\end{align*}
\end{columns}
\end{center}
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\PBzero \rightarrow \Pmu^+ \Pmu^-$ searches}
\begin{columns}
\column{5in}
\begin{itemize}
\item Background rejection power is a key feature of rare decays $\rightarrow$ use multivariate classifiers (BDT) and strong PID.
\end{itemize}
\column{0.1in}{~}
\end{columns}
\begin{columns}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{hql/BDT.png}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{hql/mass.png}
\end{columns}
\begin{itemize}
\item Normalize the BF to $\PBplus \to \PJpsi(\mu\mu) \PKplus$ and $\PBzero \to \PK \Ppi$.
\end{itemize}
\textref{ PRL 111 (2013) 101805}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Lepton non universality
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\backupend
\end{document}
mchrzasz