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\author{ {Marcin Chrzaszcz} (Universit\"{a}t Z\"{u}rich, IFJ PAN)}
\institute{UZH, IFJ PAN}
\title[Rare Decays at LHCb]{Rare Decays at LHCb}
\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\bfseries \LARGE {Rare decays at LHCb}
\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} { \Large Marcin Chrzaszcz\\\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}{LHCP, Shanghai, 15-20 May 2016}
\end{center}
\end{frame}
}
\begin{frame}{Rare Decays at LHCb}
\begin{minipage}{\textwidth}
\begin{center}
\begin{columns}
\column{0.45\textwidth}
\begin{exampleblock}{Muonic $\PB$ decays}
\ARROWR Br $\PBs/\PBd \to \mu \mu / \tau \tau$.\\
\ARROWR Br + Ang. $\PB \to \PKstar \mu \mu$.\\
\ARROWR Br + Ang. $\PBs \to \Pphi \mu \mu$.\\
\ARROWR Izospin $\PB \to \PK \mu \mu$.\\
\ARROWR CP asymmetry $\PB \to \Ppi \mu \mu$.\\
\end{exampleblock}
\column{0.45\textwidth}
\begin{alertblock}{LFU test}
\ARROW $\PBplus \to \PKplus \ell \ell$\\
\ARROW $\PBd \to \PKstar \ell \ell$\\
\end{alertblock}
\ARROW See G.Andreassi talk for LUV!!!\\
\end{columns}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\begin{columns}
\column{0.45\textwidth}
\ARROW Enormous Physics program which is constantly expanding.\\
\ARROW Will cover only part of the results.
\column{0.45\textwidth}
\begin{exampleblock}{Strange decays}
\ARROW $\PKshort \to \mu \mu$.
\end{exampleblock}
\begin{alertblock}{Radiative decays}
\ARROWR $\PB \to \PKstar \gamma$\\
\ARROWR $\PBs \to \Pphi \gamma$\\
\ARROWR $\PBs/\PBd \to \PJpsi \gamma$
\end{alertblock}
\end{columns}
\end{center}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\iffalse
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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}\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}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\only<1>{\frametitle{LHCb detector - tracking}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/sketch.png}
\end{columns}
\begin{itemize}
\item Excellent Impact Parameter (IP) resolution ($20~\rm \mu m$).\\
$\Rightarrow$ Identify secondary vertices from heavy flavour decays
\item Proper time resolution $\sim~40~\rm fs$.\\
$\Rightarrow$ Good separation of primary and secondary vertices.
\item Excellent momentum ($\delta p/p \sim 0.5 - 1.0\%$) and inv. mass resolution.\\
$\Rightarrow$ Low combinatorial background.
\end{itemize}
}
\only<2>{\frametitle{LHCb detector - PID}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/cher.png}
\end{columns}
\begin{itemize}
\item Excellent Muon identification $\epsilon_{\mu \to \mu} \sim 97\%$, $\epsilon_{\pi \to \mu} \sim 1-3\%$
\item Good $\PK-\Ppi$ separation via RICH detectors, $\epsilon_{\PK \to \PK} \sim 95\%$, $\epsilon_{\Ppi \to \PK} \sim 5\%$.\\
$\Rightarrow$ Reject peaking backgrounds.
\item High trigger efficiencies, low momentum thresholds.
Muons: $p_T > 1.76 \GeV$ at L0, $p_T > 1.0 \GeV$ at HLT1,\\
$B \to \PJpsi X $: Trigger $\sim 90\%$.
\end{itemize}
}
\textref{Int. J. Mod. Phys. A30 (2015) 1530022}
\vspace*{2.1cm}
\end{frame}
\iffalse
\begin{frame}{Observables in $\PB \to \PKstar \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\ARROW The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.\\
\ARROW The angular distribution can be written as:
\begin{tiny}
\begin{align*}
\left.\frac{1}{{\rm d}(\Gamma+\bar{\Gamma})/{\rm d}q^2}\frac{{\rm d}(\Gamma+\bar{\Gamma})}{{\rm dcos}\thetal\,{\rm dcos}\thetak\,{\rm d}\phi}\right|_{\rm P} =
\tfrac{9}{32\pi}\bigl[
&\tfrac{3}{4} (1-{F_{\rm L}})\sin^2\thetak \label{eq:pdfpwave}\\[-0.75em]
&+ {F_{\rm L}}\cos^2\thetak + \tfrac{1}{4}(1-{F_{\rm L}})\sin^2\thetak\cos 2\thetal\nonumber\\
&- {F_{\rm L}} \cos^2\thetak\cos 2\thetal + {S_3}\sin^2\thetak \sin^2\thetal \cos 2\phi\nonumber\\
&+ {S_4} \sin 2\thetak \sin 2\thetal \cos\phi + {S_5}\sin 2\thetak \sin \thetal \cos \phi\nonumber\\
&+ \tfrac{4}{3} {A_{\rm FB}} \sin^2\thetak \cos\thetal + {S_7} \sin 2\thetak \sin\thetal \sin\phi\nonumber\\
&+ {S_8} \sin 2\thetak \sin 2\thetal \sin\phi + {S_9}\sin^2\thetak \sin^2\thetal \sin 2\phi \nonumber
\bigr].
%\end{split}
%\bigr],\
\end{align*}
\end{tiny}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Link to effective operators}
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ The observables ${\color{red}{S_i}}$ are bilinear combinations of transversity amplitudes: $\apeLR,~\apaLR,~\azeLR $. \\
$\color{JungleGreen}{\Rrightarrow}$ So here is where the magic happens. At leading order the amplitudes can be written as:
{\tiny{
\eqa{
\apeLR &=&\sqrt{2} N m_B(1- \hat s)\bigg[ (\Ceff9 + \Cpeff9) \mp (\C{10} + \Cp{10})
+\frac{2\hat{m}_b}{\hat s} (\Ceff7 + \Cpeff7) \bigg]\xi_{\bot}(E_{K^*}) \nn \\[2mm]
\apaLR &=& -\sqrt{2} N m_B (1-\hat s)\bigg[(\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10})
+\frac{2\hat{m}_b}{\hat s}(\Ceff7 - \Cpeff7) \bigg] \xi_{\bot}(E_{K^*}) \nn \\[2mm]
\azeLR &=& -\frac{N m_B (1-\hat s)^2}{2 \hat{m}_{K^*} \sqrt{\hat s}} \bigg[ (\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10}) + 2\hat{m}_b (\Ceff7 - \Cpeff7) \bigg]\xi_{\|}(E_{K^*}),
\label{LargeRecoilAs}\nonumber}
}}
where $\hat s = q^2 /m_B^2$, $\hat{m}_i = m_i/m_B$. The $\xi_{\|,\bot }$ are the soft form factors. \\
\pause
$\color{JungleGreen}{\Rrightarrow}$ Now we can construct observables that cancel the $\xi$ soft 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}
% symmetries
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PB_{s/d} \to \mu \mu$}
{~}
\begin{minipage}{\textwidth}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\begin{columns}
\column{0.60\textwidth}
\ARROW Golden channel for LHCb.\\
\ARROW Normalized to the $\PB \to \PK \Ppi$ and $\PB \to \PK \PJpsi$.\\
\ARROW The selection is achived by BDT trained on MC and calibrated on data. \\
%\ARROW $\Br(\PBs \to \mu \mu) = 3.0 \pm 0.6^{+0.3}_{-0.2}$,\\
\begin{exampleblock}{\begin{small}\ARROWR $\Br(\PBs \to \mu \mu) =( 3.0 \pm 0.6^{+0.3}_{-0.2})10^{-9}$\end{small}
}
$7.8~\sigma$ significant!
\end{exampleblock}
\begin{alertblock}{}
\begin{small}\ARROWR $\Br(\PBd \to \mu \mu) < 3.4 \times 10^{-10}$, $90\%\rm CL$\end{small}
\end{alertblock}
\begin{exampleblock}{Effective lifetime}
\ARROWR Sensitivity to non-scalar NP.\\
\ARROWR $\tau(\PBs \to \mu\mu)=2.04\pm0.44\pm0.05 \rm ps$
\end{exampleblock}
\column{0.40\textwidth}
\includegraphics[width=0.90\textwidth]{images/hidef_Fig1.png}\\
\only<1>{
\includegraphics[width=0.90\textwidth]{images/hidef_Fig22.png}\\
\includegraphics[width=0.90\textwidth]{images/hidef_Fig20.png}
}
\only<2>{
\includegraphics[width=0.9\textwidth]{images/life.png}\\
\includegraphics[width=0.9\textwidth]{images/hidef_Fig2bot.png}\\
}
\end{columns}
\end{center}
\end{minipage}
\textref{arXiv:1703.05747}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PB_{s/d} \to \tau \tau$}
{~}
\begin{minipage}{\textwidth}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\begin{columns}
\column{0.50\textwidth}
\ARROW NP sensitivity enhanced due to the high $\tau$ mass.\\
\ARROW More challenging: at least 2$\nu$ are escaping.\\
\ARROW Selecting $\tau \to 3\pi \nu$, $\rightarrow~9.31~\%$\\
\ARROW Normalization channel: $\PB \to \PD(\PK \pi \pi) \PDs(\PK \PK \pi)$.\\
\ARROW No peak in the $\PB$ mass window $\rightarrow$ fit the NN output.
\includegraphics[width=0.85\textwidth]{images/hidef_Fig7.png}
\column{0.50\textwidth}
\includegraphics[width=0.85\textwidth]{images/hidef_Fig11.png}\\
\includegraphics[width=0.85\textwidth]{images/hidef_Fig2a.png}\\
\end{columns}
\end{center}
\end{minipage}
\textref{arXiv:1703.02508}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\Lambda_b \to p \pi \mu \mu$}
{~}
\begin{minipage}{\textwidth}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\begin{columns}
\column{0.60\textwidth}
\ARROW First observation of $b \to d$ in baryon system!\\
\ARROW BDT selection trained on MC\\
\ARROW Normalized to $\Lambda_b \to p \pi \PJpsi$\\
\ARROW With futher QCD improvements we will be able to to measure $\frac{\vert V_{ts}\vert }{\vert V_{td}\vert}$.
\begin{exampleblock}{\begin{small}\ARROWR $\frac{\Br(\Lambda_b \to p \pi \mu \mu)}{\Br(\Lambda_b \to p \pi \PJpsi)} =0.044 \pm 0.012 \pm 0.007$\end{small}
}
\ARROWR $5.5~\sigma$ significance! \ARROWR First observation.\\
\end{exampleblock}
\includegraphics[width=0.71\textwidth]{images/hidef_Fig3.png}
\column{0.50\textwidth}
\includegraphics[width=0.95\textwidth]{images/dupa.png}\\
\includegraphics[width=0.95\textwidth]{images/hidef_Fig2.png}\\
\begin{alertblock}{}\begin{small}
$\Br(\Lambda_b \to p \pi \mu \mu) = (6.9 \pm 1.9 \pm 1.1^{+1.3}_{-1.0} ) \times 10^{-8}$
\end{small}
\end{alertblock}
\end{columns}
\end{center}
\end{minipage}
\textref{J. High Energy Phys. 04 029}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Search for light scalars}
{~}
\begin{minipage}{\textwidth}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\begin{columns}
\column{0.55\textwidth}
\ARROW Hidden sector models are gathering more and more attention.\\
\ARROW Inflaton model: new scalar then mixes with the Higgs.\\
\ARROW $\PB$ decays are sensitive as the inflaton might be light.\\
\ARROW Searched for long living particle $\chi$ produced in: $\PB \to \chi(\mu\mu) \PK$.\\
\ARROW Analysis performed blindly as a peak search.\\
\ARROW Light inflaton essentially ruled out:\\
\includegraphics[width=0.75\textwidth]{{images/hidef_Inflaton_parameter_space_log_PAPER}.png}\\
\column{0.45\textwidth}
\includegraphics[width=0.95\textwidth]{images/hidef_diagram.png}\\
\includegraphics[width=0.95\textwidth]{images/hidef_excluded_limit2D.png}
\end{columns}
\end{center}
\end{minipage}
\textref{Phys. Rev. D 95, 071101 (2017)}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PKshort \to \mu \mu$}
{~}
\begin{minipage}{\textwidth}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{center}
\begin{columns}
\column{0.60\textwidth}
\ARROW $\Pproton \Pproton$ collisions create enormous amount of strange messons.\\
\ARROW Can be used to search for $\PKshort \to \mu \mu$.\\
\ARROW SM prediction: $\Br(\PKshort \to \mu \mu)= (5.0 \pm 1.5) \times 10^{-12}$\\
\ARROW Dominated by the long distance effects.\\
\ARROW We used two types of triggers: TIS and TOS.\\
\ARROW Bkg dominated by $\PKshort \to \pi \pi$.
\includegraphics[width=0.75\textwidth]{{images/hidef_Fig222}.png}\\
\column{0.4\textwidth}
\includegraphics[width=0.95\textwidth]{images/hidef_Fig6.png}\\
\ARROWR No significant enhanced of signal has been observed and UL was set:
\begin{alertblock}{}\begin{small}
$\Br(\PKshort \to \mu \mu) <6.9 (5.8) \times 10^{-9}$ at $95 (90)\%$ CL
\end{small}
\end{alertblock}
\end{columns}
\end{center}
\end{minipage}
\textref{CONF-2016-013}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$ decay }
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{0.55\textwidth}
\ARROW $\PBzero \to \PKstar \Pmuon \APmuon$ is a smoking gun for NP hunting!\\
\ARROW Reach angular observables makes is sensitive to different NP models\\
\ARROW In addition one can construct less form factor dependent observables:
\begin{equation}
P_5^{\prime}=\frac{S_5}{\sqrt{F_L(1-F_L)}}\nonumber
\end{equation}
\ARROW In single analysis observed $3.4~\sigma$ discrepancy in the $C_9$ WC.
\column{0.45\textwidth}
\includegraphics[angle=-90,width=0.9\textwidth]{images/P5p.pdf} \\
\includegraphics[angle=-90,width=0.9\textwidth]{images/AFBPad.pdf}
\end{columns}
\end{minipage}
\textref{JHEP 02 (2016) 104}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PBs \to \Pphi \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[height=4cm]{images/bs2phipi.png}
\includegraphics[height=4cm]{images/BsSel.png}
\end{center}
\begin{itemize}
\item Recent LHCb measurement, \href{https://cds.cern.ch/record/2029820/files/JHEP09-179.pdf}{{\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.
\item Angular part in agreement with SM ($S_5$ is not accessible).
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\Lambda_b \to \Lambda \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\only<1>{
\includegraphics[width=0.65\textwidth]{images/Lb_BR.png}
}
\only<2>{
\includegraphics[width=0.45\textwidth]{images/Lblow.png}
\includegraphics[width=0.45\textwidth]{images/Lbhigh.png}
}
\end{center}
\begin{itemize}
\item This years LHCb measurement \href{http://arxiv.org/abs/1503.07138}{{\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}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Theory implications of $b \to s \ell \ell$}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item A fit prepared by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}.
\item The data can be explained by modifying the $C_9$ Wilson coefficient.
\item Overall there is $>4~\sigma$ discrepancy wrt. the SM prediction.
\end{itemize}
\includegraphics[width=0.9\textwidth]{images/FIT.png}
\end{minipage}
\textref{JHEP 06 (2016) 092}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{If not NP?}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item We are not there yet!
\item There might be something not taken into account in the theory.
\item Resonances ($\PJpsi$, $\Ppsi(2S)$) tails can mimic NP effects.
\item There might be some non factorizable QCD corrections.\\
'' However, the central value of this effect would have to be significantly larger than expected on the basis of existing estimates'' \texttt{D.Straub}, \href{http://arxiv.org/abs/1503.06199}{ {\color{blue}{arXiv:1503.06199}}}.
\end{itemize}
\only<1>{
\includegraphics[width=0.6\textwidth]{images/charmloop.png}
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Theory implications 2}
\begin{minipage}{\textwidth}
{~}
\ARROW If one includes recent measurements of $R_k$ and $R_{\PKstar}$:
\begin{center}
\includegraphics[width=0.99\textwidth]{images/quim1.png}
\end{center}
\begin{columns}
\column{0.5\textwidth}
\includegraphics[width=0.75\textwidth]{images/quim2.png}
\column{0.5\textwidth}
\includegraphics[width=0.75\textwidth]{images/quim3.png}
\end{columns}
\ARROW Strong indications of NP!
\end{minipage}
\textref{arxiv::1704.05340}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Measurement of phase difference}
\begin{minipage}{\textwidth}
{~}
\begin{columns}
\column{0.6\textwidth}
\ARROW One could try to measure the phase difference between the resonances and the nonresonant amplitudes to see if the interference is large enough to explain the effects.\\
\ARROW Measured firstly done for the decay $\PB \to \PK \mu \mu$.\\
\ARROW The analysis based:
\begin{equation}
C_9^{\rm eff} = C_9 +Y(q^2) = C_9 +\sum_j \eta_j e^{i \delta_i} A_j^{\rm res}(q^2)\nonumber
\end{equation}
\ARROW The amplitudes are modelled Briet-Wigner and Flatte functions.\\
\ARROW Interference cannot explain the observed anomalies.
\column{0.4\textwidth}
\includegraphics[width=0.65\textwidth]{images/charm.png}\\
\includegraphics[width=0.75\textwidth]{{images/hidef_finalplot_pos_neg}.png}\\\includegraphics[width=0.7\textwidth]{images/hidef_WilsonProfile.png}
\end{columns}
\end{minipage}
\textref{Phys. Rev. D 95, 071101 (2017)}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Conclusions}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item Clear tensions wrt. SM predictions!
\item Measurements cluster in the same direction.
\item We are not opening the champagne yet!
\item Still need improvement both on theory and experimental side.
\item Time will tell if this is QCD+fluctuations or new Physics:
\end{itemize}
\pause
''... when you have eliminated all the\\
Standard Model explanations, whatever remains,\\
however improbable, must be New Physics.''\\
Prof. Joaquim Matias
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\begin{LARGE}
Thank you for the attention!
\end{LARGE}
\includegraphics[width=0.8\textwidth]{images/Joke.jpg}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\backupbegin
\begin{frame}\frametitle{Backup}
\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}{$\PBzero \to \PKstar \Pmuon \APmuon$ kinematics}
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.
\only<1>{
\begin{columns}
\column{0.5\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ $\cos \thetak$: the angle between the direction of the kaon in the $\PKstar$ ($\overline{\PK}^{\ast}$) rest frame and the direction of the $\PKstar$ ($\overline{\PK}^{\ast}$) in the $\PBzero$ ($\APBzero$) rest frame.\\
$\color{JungleGreen}{\Rrightarrow}$ $\cos \thetal$: the angle between the direction of the $\Pmuon$ ($\APmuon$) in the dimuon rest frame and the direction of the dimuon in the $\PBzero$ ($\APBzero$) rest frame.\\
$\color{JungleGreen}{\Rrightarrow}$ $\phi$: the angle between the plane containing the $\Pmuon$ and $\APmuon$ and the plane containing the kaon and pion from the $\PKstar$.
\column{0.5\textwidth}
\includegraphics[width=0.99\textwidth]{images/angles.png}
\end{columns}
}
\only<2>{
{\tiny{
\eqa{\label{dist}
\frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi}&=&\frac9{32\pi} \bigg[
{\color{red}{J_{1s}}} \sin^2\theta_K + {\color{red}{J_{1c}}} \cos^2\theta_K + ({\color{red}{J_{2s} }}\sin^2\theta_K + {\color{red}{J_{2c}}} \cos^2\theta_K) \cos 2\theta_l\nn\\[1.5mm]
&&\hspace{-2.7cm}+ {\color{red}{J_3}} \sin^2\theta_K \sin^2\theta_l \cos 2\phi + {\color{red}{J_4}} \sin 2\theta_K \sin 2\theta_l \cos\phi + {\color{red}{J_5}} \sin 2\theta_K \sin\theta_l \cos\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ ({\color{red}{J_{6s}}} \sin^2\theta_K + {\color{red}{{J_{6c}}}} \cos^2\theta_K) \cos\theta_l
+ {\color{red}{J_7}} \sin 2\theta_K \sin\theta_l \sin\phi + {\color{red}{J_8}} \sin 2\theta_K \sin 2\theta_l \sin\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ {\color{red}{J_9}} \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,,
\nonumber}
}}\\{~}\\
$\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decay.\\
$\color{JungleGreen}{\Rrightarrow}$ The $CP$ averaged angular observables are defined:\\
\eq{
S_i = \dfrac{J_i+ \bar{J}_i}{(d \Gamma + d \bar{\Gamma})/dq^2}\nonumber
}
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Link to effective operators}
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ The observables ${\color{red}{J_i}}$ are bilinear combinations of transversity amplitudes: $\apeLR,~\apaLR,~\azeLR $. \\
$\color{JungleGreen}{\Rrightarrow}$ So here is where the magic happens. At leading order the amplitudes can be written as:
{\tiny{
\eqa{
\apeLR &=&\sqrt{2} N m_B(1- \hat s)\bigg[ (\Ceff9 + \Cpeff9) \mp (\C{10} + \Cp{10})
+\frac{2\hat{m}_b}{\hat s} (\Ceff7 + \Cpeff7) \bigg]\xi_{\bot}(E_{K^*}) \nn \\[2mm]
\apaLR &=& -\sqrt{2} N m_B (1-\hat s)\bigg[(\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10})
+\frac{2\hat{m}_b}{\hat s}(\Ceff7 - \Cpeff7) \bigg] \xi_{\bot}(E_{K^*}) \nn \\[2mm]
\azeLR &=& -\frac{N m_B (1-\hat s)^2}{2 \hat{m}_{K^*} \sqrt{\hat s}} \bigg[ (\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10}) + 2\hat{m}_b (\Ceff7 - \Cpeff7) \bigg]\xi_{\|}(E_{K^*}),
\label{LargeRecoilAs}\nonumber}
}}
where $\hat s = q^2 /m_B^2$, $\hat{m}_i = m_i/m_B$. The $\xi_{\|,\bot }$ are the soft form factors. \\
\pause
$\color{JungleGreen}{\Rrightarrow}$ Now we can construct observables that cancel the $\xi$ soft 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}
% symmetries
\begin{frame}{Symmetries in $\PB \to \PKstar \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ We have 12 angular coefficients ($S_i$).\\
$\color{JungleGreen}{\Rrightarrow}$ There exist 4 symmetry transformations that leave the angular distributions unchanged:
\begin{tiny}
\eq{
n_\|=\binom{A_\|^L}{A_\|^{R*}}\ ,\quad
n_\bot=\binom{A_\bot^L}{-A_\bot^{R*}}\ ,\quad
n_0=\binom{A_0^L}{A_0^{R*}}\ .\nonumber
}
\end{tiny}
\begin{tiny}
\eq{
n_i^{'} = U n_i=
\left[
\begin{array}{ll}
e^{i\phi_L} & 0 \\
0 & e^{-i \phi_R}
\end{array}
\right]
\left[
\begin{array}{rr}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta
\end{array}
\right]
\left[
\begin{array}{rr}
\cosh i \tilde{\theta} & -\sinh i \tilde{\theta} \\
- \sinh i \tilde{\theta} & \cosh i \tilde{\theta}
\end{array}
\right]
n_i \,.
\label{symmassless}\nonumber}
\end{tiny}
$\color{JungleGreen}{\Rrightarrow}$ Using this symmetries one can show that there are 8 independent observables. The pdf can be written as:
\begin{tiny}
\begin{align*}
\left.\frac{1}{{\rm d}(\Gamma+\bar{\Gamma})/{\rm d}q^2}\frac{{\rm d}(\Gamma+\bar{\Gamma})}{{\rm dcos}\thetal\,{\rm dcos}\thetak\,{\rm d}\phi}\right|_{\rm P} =
\tfrac{9}{32\pi}\bigl[
&\tfrac{3}{4} (1-{F_{\rm L}})\sin^2\thetak \label{eq:pdfpwave}\\[-0.75em]
&+ {F_{\rm L}}\cos^2\thetak + \tfrac{1}{4}(1-{F_{\rm L}})\sin^2\thetak\cos 2\thetal\nonumber\\
&- {F_{\rm L}} \cos^2\thetak\cos 2\thetal + {S_3}\sin^2\thetak \sin^2\thetal \cos 2\phi\nonumber\\
&+ {S_4} \sin 2\thetak \sin 2\thetal \cos\phi + {S_5}\sin 2\thetak \sin \thetal \cos \phi\nonumber\\
&+ \tfrac{4}{3} {A_{\rm FB}} \sin^2\thetak \cos\thetal + {S_7} \sin 2\thetak \sin\thetal \sin\phi\nonumber\\
&+ {S_8} \sin 2\thetak \sin 2\thetal \sin\phi + {S_9}\sin^2\thetak \sin^2\thetal \sin 2\phi \nonumber
\bigr].
%\end{split}
%\bigr],\
\end{align*}
\end{tiny}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\backupend
\end{document}
Marcin Chrzaszcz