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%                           Introduction
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\usetheme{Sybila} 

\title[ Rare beauty and charm decays at LHCb]{ Rare beauty and charm decays at LHCb}
\author{Marcin Chrz\k{a}szcz$^{1,2}$ \\ \footnotesize{on behalf of the LHCb collaboration}}
\institute{$^1$~University of Zurich,\\ $^2$~Institute of Nuclear Physics, Krakow \\{~}\\  Heavy Quarks and Leptons 2014 }
\date{\today}
\begin{document}
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\frame[plain]{\titlepage}
\author{Marcin Chrz\k{a}szcz}
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\institute{~(UZH, IFJ)}

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%                          OUTLINE
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\section[Outline]{}
\begin{frame}
%\tableofcontents
%FIXME!
\begin{enumerate}
\item Rare $\PB$ decays:
\begin{itemize}
\item $\PB \to \PK \Ppi \Ppi \Pphoton$
\item $\PB \to \mu \mu$.
\item $\Pbeauty \to \Pstrange \Plepton \Plepton$.
\end{itemize}
\item Charm decays:
\begin{itemize}
\item $\PD \to \mu \mu$.
\end{itemize}
\end{enumerate}

\end{frame}

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%                          Introduction
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%\section{LHCb detector}

%\begin{frame}\frametitle{LHCb detector}
%\begin{columns}
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%\includegraphics[width=0.98\textwidth]{det.jpg}
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%\begin{footnotesize}


 %     LHCb is a forward spectrometer:
 %       	\begin{itemize}
 %       	\item Excellent vertex resolution.
 %       	\item Efficient trigger.
 %       	\item High acceptance for $\Ptau$ and $\PB$.
 %       	\item Great Particle ID
 %       	\end{itemize}	
        


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%\end{columns}

%\end{frame}

\section{Introduction}

\begin{frame}\frametitle{Why rare decays?}
\begin{columns}
\column{4in}
\begin{itemize}
\item CKM structure in SM allows only the charged interactions to change flavour.
\begin{itemize}
\item Other interactions are flavour conserving.
\end{itemize} 
\item One can escape the CKM structure and produce $\Pbottom \to \Pstrange$ and $\Pbottom \to \Pdown$ only at loop level.
\begin{itemize}
\item This kind of processes are suppressed in SM $\to$~Rare decays.
\end{itemize}
\end{itemize}
\begin{center}
\includegraphics[scale=0.3]{hql/lupa.png}
\includegraphics[scale=0.3]{hql/example.png}
\end{center}
\column{1.5in}
\includegraphics[width=0.62\textwidth]{hql/couplings.png}
\end{columns}

\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{3.2in}
\begin{align*} 
H_{eff} = - \dfrac{4G_f}{\sqrt{2}} V V^{\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*}

\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}
\begin{center}
\includegraphics[width=0.85\textwidth,height=3cm]{hql/all.png}

\end{center}


\end{frame}



\begin{frame}\frametitle{Radiative decays}

\begin{columns}
\column{5in}

\begin{itemize}
\item $\PBzero \to \PKstar \Pphoton$ - first observed penguin!
\begin{itemize}
\item CLEO, [\href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.674}{\color{blue}PRL, 71 (1993) 674}]
\end{itemize}
\item B-factories probed NP measuring, inclusively/ semi-inclusively  $\mathcal{B}(\Pbeauty \to \Pstrange \Pphoton)$
\end{itemize}
\column{0.1in}{~}

\end{columns}



\begin{columns}
\column{3in}
\begin{itemize}
\item Is there anyway LHCb can contribute?
\begin{itemize}
\item Measurements of $\mathcal{B}(\Pbeauty \to \Pstrange \Pphoton)$ very difficult.
\item Can probe probe polarization!
\end{itemize}
\end{itemize}
\column{2in}
\includegraphics[width=0.85\textwidth]{hql/btosgamma.png}
\end{columns}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5


\begin{columns}
\column{5in}

\begin{itemize}
\item In SM, photons form $\Pbeauty \to \Pstrange \Pphoton$ decays are left handed.
\begin{itemize}
\item Charged current interactions: $C_7/C'_7\sim m_{\Pbeauty}/m_{\Pstrange}$
\end{itemize}
\item Can test $C_7/C'_7$ using:
\begin{itemize}
\item Mixing induced CP violation: \href{http://arxiv.org/abs/hep-ph/9704272}{\color{blue}Atwood et. al. PRL 79 (1997) 185-188}
\item $\PLambdab$ baryons: \href{http://arxiv.org/abs/hep-ph/0108074}{\color{blue}Hiller \& kagan PRD 65 (2002) 074038}
\end{itemize}
\end{itemize}
\column{0.1in}{~}

\end{columns}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5

\begin{frame}\frametitle{Photon polarization from $\color{white} B^+ \to K^{+} \pi^- \pi^+ \gamma$}


\begin{columns}
\column{3.5in}

\begin{itemize}
\item OR: Study $\PB \to \PK^{\ast \ast} \Pphoton$ decays like $\PBplus \to \PK_1(1270) \Pphoton$
\begin{itemize}
\item \href{http://arxiv.org/abs/hep-ph/0205065}{\color{blue}Gronau \& Pirjol PRD 66 (2002) 054008}
\end{itemize}
\item The trick is to get the photon polarization from the up-down asymmetry of photon direction in the $\PK \Ppi \Ppi$ rest frame. 
\begin{itemize}
\item No asymmetry $\rightarrow$ Unpolarised photons.
\end{itemize}
\item Conceptionally this measurement is similar to the Wu experiment, which first observed parity violation.


\end{itemize}
\column{1.5in}

\includegraphics[width=0.95\textwidth]{hql/polarization.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\color{white} B^+ \to K^{+} \pi^- \pi^+ \gamma$ at LHCb}


\begin{columns}
\column{3.in}

\begin{itemize}
\item LHCb looked at $\PBplus \to \PKplus \Ppiminus \Ppiplus \Pphoton$, using un-converted photons.
\item Got over 13.000 candidates in $3~fb^{-1}$!
\item \href{http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.161801}{\color{blue} Phys. Rev. Lett. 112, 161801 }
\item $\PKplus \Ppiminus \Ppiplus$ system has variety of resonances.
\begin{itemize}
\item $\PK \Ppi \Ppi \Ppi$system studied inclusively.
\item Bin the mass and look for polarization there.
\end{itemize}
\end{itemize}
\column{2in}
{~}
\includegraphics[width=0.95\textwidth]{hql/plotspolarization.png}

\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}%\frametitle{$\color{white} B^+ \to K^{+} \pi^- \pi^+ \gamma$ at LHCb}
\begin{center}
{\color{red} Fit with $\color{red}(C_7'-C_7)/(C_7'+C_7)=0$}, {\color{blue} Best fit}
\includegraphics[width=0.93\textwidth]{hql/photonfit.png}
\end{center}


\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Up-down asymmetry}

\begin{columns}
\column{3.in}

\begin{itemize}
\item Combining the 4 bins, gives $5.2\sigma$ significance from no photon polarization hypothesis.
\item Unfortunately without understanding the hadron system it is impossible to tell if the photon is left or right -handed.
\end{itemize}

\column{2in}
{~}
\includegraphics[width=0.95\textwidth]{hql/aud.png}

\end{columns}
\begin{center}
$\rightarrow$~ First observation of photon polarization in $\Pbeauty \to \Pstrange \Pphoton$!

\end{center}



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\color{white}B^0 \rightarrow \mu^+ \mu^-$}
\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: $\mathcal{B}(\PBs \to \Pmuon \APmuon) \sim \tan^6 \beta /m_A^4$ 
\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{\color{white} $\color{white}B^0 \rightarrow \mu^+ \mu^-$ 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}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{\color{white} $\color{white}B^0 \rightarrow \mu^+ \mu^-$ 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 $2.1~fb^{-1}$.
\end{itemize}
\item Summer 2013:
\begin{itemize}
\item Full data sample: $3~fb^{-1}$.
\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}


\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{LHCb+CMS Combination}
\begin{Large}


\begin{center}
$\mathcal{B}(\PBs \to \Pmuon \APmuon) =(2.9 \pm 0.7 )\times 10^{-9}$\\
$\mathcal{B}(\PBzero \to \Pmuon \APmuon) =(3.6^{+1.6}_{-1.4} )\times 10^{-10}$
\end{center}
\end{Large}

\includegraphics[width=0.95\textwidth]{hql/limits.png}

Full combination CMS+LHCb with simultaneous fit close to completion!
\begin{itemize}
\item \href{https://cds.cern.ch/record/1564324/files/LHCb-CONF-2013-012.pdf}{\color{blue}LHCb-CONF-2013-012}
\end{itemize}

\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\color{white}B^{0} \rightarrow K^{\ast} \mu \mu$ angular distributions}
\begin{columns}
\column{2.5in}{~}
\begin{itemize}
\item Can probe photon polarization using virtual photons in $\Pbeauty \to \Pstrange \Plepton \Plepton$.
\item LHCb favourite: $\PBzero \to \PKstar \mu \mu$.
\item Sensitive to lot of new physics models.
\item Decay described by three angles $\theta_l, \theta_K, \phi$ and dimuon invariant mass $q^2$.
\item Analysis is performed in bins of $q^2$.
\end{itemize}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{hql/angles.png}

\end{columns}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\color{white}B^{0} \rightarrow K^{\ast} \mu \mu$ angular distributions}
\begin{itemize}
\item Angular distributions depends on 11 angular terms:
\includegraphics[width=0.95\textwidth]{hql/eq.png}
\end{itemize}
where the $J_i$ are bilinear combinations of helicity amplitudes.
\begin{itemize}
\item Not enough events in our data sample to fit for 11 parameters $\rightarrow$ need to simplify!
\item Can use symmetries, to reduced the the parameters \\ to 9 $\rightarrow$ still a bit large!
\end{itemize}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\color{white}B^{0} \rightarrow K^{\ast} \mu \mu$ Folding}
\begin{itemize}
\item One can simplify the angular distribution by folding: eg. $\phi \to \phi +\pi$ for ($\phi<0$).
\item Cancels terms with $\cos \phi$ and $\sin \phi$.

\end{itemize}
\includegraphics[width=0.95\textwidth]{hql/eq2.png}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\color{white}B^{0} \rightarrow K^{\ast} \mu \mu$ angular distributions }
\begin{itemize}
\item Different foldings cancel different angular observables. \href{http://arxiv.org/abs/1308.1707}{\color{blue}[PRL 111 191801 (2013)]}
\includegraphics[width=0.95\textwidth]{hql/ps.png}
\item Observables $P'_{4,5} = S_{4,5}/\sqrt{F_L(1-F_L)}$
\item Leading form-factor uncertainties cancel.
\item In $1~fb^{-1}$, LHCb observes a local discreapncy of $3.7\sigma$ in $P'_5$.
\item Probability that at least one bin varies by this much is $0.5\%$.
\item SM prediction form: \href{http://arxiv.org/abs/1303.5794}{\color{blue} JHEP 05 (2013) 137}

\end{itemize}

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Understanding the $\color{white}B^{0} \rightarrow K^{\ast} \mu \mu$ anomaly 1/2}
\begin{columns}
\column{3.5in}
\begin{itemize}
\item Matias, Decotes-Genon \& Virto performed a global fit to the avaible $\Pbeauty \to \Pstrange \Pphoton$ abd $\Pbeauty \to \Pstrange \Plepton \Plepton$.
\item Found $4.5 \sigma$ discrepancy from SM.
\item Fit favours $C_9^{NP}=1.5$
\item \href{http://arxiv.org/abs/1307.5683}{\color{blue} PRD 88 074002 (2013)}
\end{itemize}
\begin{itemize}
\item Straub \& Altmannshofer performed a global analysis and found discrepancies at the level of $3\sigma$. Data again best describes a modified $C_9$. 
\item Data can be explained by introducing a flavour changing $\PZprime$ boson, with mass $\mathcal{O}(10~TeV)$
\item \href{http://arxiv.org/abs/1212.2263}{\blue{EPJC 73 2646 (2013)}}
\end{itemize}

\column{1.5in}
\includegraphics[width=0.9\textwidth]{hql/np.png}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{frame}\frametitle{Understanding the $\color{white}B^{0} \rightarrow K^{\ast} \mu \mu$ anomaly 2/2}
%\begin{columns}
%\column{3in}

%\includegraphics[width=0.99\textwidth]{hql/c9.png}
%\column{2in}
%\begin{itemize}
%\item High $q^2$ differential BF suggests are all below SM. 
%\item Better consistency with $C_9^{NP}=-1.5$
%\end{itemize}

%\end{columns}


%\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Lepton universality}
\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]{hql/uni2.png}
\item Challenging analysis.
\item Migration of events modeled by MC.
\item Correct bremsstrahlung.
\item Take double ratio with $\PBplus \to \PJpsi \PKplus$ to cancel systematics.
\item In $3fb^{-1}$, 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]{hql/universality.png}
\end{columns}
\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{FCNC in charm decays}
\begin{columns}
\column{3.0in}
\begin{itemize}
\item GIM cancelation effective in  $\Pcharm \to \Pup$ transitions due to small size of $m_b$.
\item SM prediction:~$\mathcal{B}(\PDzero \to \mu \mu) \sim  6 \times 10^{-11}$


\end{itemize}
\column{1.5in}
\includegraphics[width=0.9\textwidth]{hql/ds2mumu.png}
\end{columns}
\includegraphics[width=0.9\textwidth]{hql/ds2mumu2.png}
\begin{small}

\begin{itemize}
\item Use $\PDstar^{\pm}$ and exploit small $\Delta m$  for background suppression.
\item Limitation is $\pi \to \mu$ mis-id.
\item Limit: $\mathcal{B}(\PDzero \to \mu \mu)<6.2\times 10^{-9}$ at $90\%$ CL
\item \href{http://arxiv.org/abs/1305.5059}{\color{blue} PLB 725 (2013) 15-24}
\end{itemize}

\end{small}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Conclusions}
\begin{columns}
\column{3.2in}
\begin{itemize}
\item Rare decays play important role in hutting NP.
\item Can access NP scales beyond reach of GPD.
\item Tension in $\Pbeauty \to \Pstrange \Plepton \Plepton$, theory correct?
\item List of decays presented in this talk is just a tip of iceberg:
\begin{itemize}
\item Please look at ours: isospin, $A_{CP}$.
\item More are on their way.
\end{itemize}


\end{itemize}
\column{2in}
\includegraphics[width=0.9\textwidth]{hql/higgs_boring.png}
\end{columns}

\end{frame}


\end{document}
