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% particles
\def\LstFTTT {\ensuremath{\PLambda^{*}(1520)^{0}}\xspace}
\def\dll {\ensuremath{\mathrm{DLL}}\xspace}
\def\Lb {\ensuremath{\PLambda_b}}
% useful decays
\def\BdToKpimm {\decay{\Bd}{\Kp\pim\mumu}}
\def\BuToKmm {\decay{\Bu}{\Kp\mumu}}
\def\BsToJPsiKst {\decay{\Bs}{\jpsi\Kstarz}}
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% interesting variables
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%% peaking background mass hypotheses
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%% some other decays
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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich, IFJ PAN)}
\institute{UZH}
\title[Rare B Decays: Theory and Experiment 2016]{Rare B Decays: Theory and Experiment 2016}
\date{18 April 2016}
\begin{document}
\tikzstyle{every picture}+=[remember picture]
{
\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
\begin{frame}[c]%{\phantom{title page}}
\begin{center}
\begin{center}
\begin{columns}
\begin{column}{0.9\textwidth}
\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Recent results \\from LHCb
}
\end{column}
\begin{column}{0.2\textwidth}
%\includegraphics[width=\textwidth]{SHiP-2}
\end{column}
\end{columns}
\end{center}
\quad
\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
\end{column}
\begin{column}{0.53\textwidth}
\includegraphics[height=1.3cm]{uzh-transp}{~}{~}
\includegraphics[height=1.1cm]{ifj.png}
\end{column}
\end{columns}
\vspace{1em}
% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, LeD. Gorbunov}\normalsize\\
\vspace{0.5em}
\textcolor{normal text.fg!50!Comment}{Barcelona, \\April 18, 2016}
\end{center}
\end{frame}
}
\begin{frame}{Outline}
\begin{minipage}{\textwidth}
{~}\\
\begin{enumerate}
\item LHCb detector.
\item Angular analysis of $\PBd \to \PKstar \Pmu \Pmu$.
\item Other LHCb EWP measurements.
\item Glimpse into the future.
\end{enumerate}
\end{minipage}
\vspace*{2.cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Why flavour physics
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DETECTOR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\only<1>{\frametitle{LHCb detector - tracking}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/sketch.png}
\end{columns}
\begin{itemize}
\item Excellent Impact Parameter (IP) resolution ($20~\rm \mu m$).\\
$\Rightarrow$ Identify secondary vertices from heavy flavour decays
\item Proper time resolution $\sim~40~\rm fs$.\\
$\Rightarrow$ Good separation of primary and secondary vertices.
\item Excellent momentum ($\delta p/p \sim 0.4 - 0.6\%$) and inv. mass resolution.\\
$\Rightarrow$ Low combinatorial background.
\end{itemize}
}
\only<2>{\frametitle{LHCb detector - particle identification}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/cher.png}
\end{columns}
\begin{itemize}
\item Excellent Muon identification $\epsilon_{\mu \to \mu} \sim 97\%$, $\epsilon_{\pi \to \mu} \sim 1-3\%$
\item Good $\PK-\Ppi$ separation via RICH detectors, $\epsilon_{\PK \to \PK} \sim 95\%$, $\epsilon_{\Ppi \to \PK} \sim 5\%$.\\
$\Rightarrow$ Reject peaking backgrounds.
\item High trigger efficiencies, low momentum thresholds.
Muons: $p_T > 1.76 \GeV$ at L0, $p_T > 1.0 \GeV$ at HLT1,\\
$B \to \PJpsi X $: Trigger $\sim 90\%$ efficient.
\end{itemize}
}
\end{frame}
\begin{frame}{Analysis of Rare decays}
\begin{footnotesize}
\only<1>{
%{\Large Since a long time ago...} \\ \medskip
%\hspace*{1.4cm}$\Rightarrow$ $b \to s \gamma$ and $b \to s \ell\ell $ {\bf Flavour Changing Neutral Currents} have been used as {\bf \cred Our Portal} \\ to explore the fundamental theory beyond SM. \\
%\medskip
%\medskip
%\hfill....... with not much success till 2013.\hspace*{1cm}
%\bigskip
Analysis of FCNC in a model-independent approach, effective Hamiltonian:
\vspace*{-0.1cm}
\begin{columns}
\begin{column}{1cm}
~
\end{column}
\begin{column}{8cm}
\begin{equation*}
b\to s\gamma(^*): {\mathcal H}^{SM}_{\Delta F=1} \propto
\sum_{i=1}^{10} V_{ts}^* V_{tb} {\cgreen \C{i}} \alert{ {\cal O}_i} + \ldots
\end{equation*}
\vspace{-0.2cm}
\begin{itemize}
\item $\alert{ {\cal O}_7} = \frac{e}{16 \pi^2}m_b\,
(\bar s\sigma^{\mu\nu} P_R b) F_{\mu\nu}\,$ %\quad [real or soft photon]
\item $\alert{ {\cal O}_9}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b)\ (\bar\ell\gamma_\mu\ell)$
%\quad [$b\to s\mu\mu$ via $Z$/hard $\gamma$]
\item $\alert{ {\cal O}_{10}}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b) \ (\bar\ell\gamma_\mu\gamma_5\ell)$, ...
%\quad [$b\to s\mu\mu$ via $Z$]
\end{itemize}
\end{column}
\begin{column}{5.5cm}
\includegraphics[width=3.5cm]{images/qum1.png}
%\includegraphics[width=3cm]{bsll.pdf}
\end{column}
\end{columns}
%\hspace*{5cm} with no clear success yet...
%\bigskip
%\centerline{{\bf Goal}: \underline{Decode the short distance physics to find a smoking gun of BSM}\hspace*{2cm}}
\bigskip
\hspace*{0.0cm} $\bullet$ {\bf SM} Wilson coefficients up to NNLO + e.m. corrections at $\mu_{ref}=4.8$ GeV [{\cgreen Misiak et al.}]: $${\cal C}_7^{\rm SM}=-0.29,\, {\cal C}_9^{\rm SM}=4.1,\, {\cal C}_{10}^{\rm SM}=-4.3$$
%BUT, like in the film there is always the good, the bad and the ugly.
\bigskip
$\bullet$ {\bf NP} changes short distance ${\cal C}_i-{\cal C}_i^{\rm SM}={\cal C}_i^{\rm NP}$ and induce new operators, like ${\cal O}^\prime_{7,9,10}={\cal O}_{7,9,10}\,\, (P_L \leftrightarrow P_R)$ ... also scalars, pseudoescalar, tensor operators...%\bigskip
}
\only<2>
{
\begin{center}
\includegraphics[width=0.5\textwidth]{images/joke.jpg}
\end{center}
}
\end{footnotesize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
LHCb measurement of $\PBd \to \PKstar \Pmu \Pmu$
\end{Huge}
\end{center}
\end{frame}
\iffalse
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{LHCbs $\PBzero \to \PKstar \Pmuon \APmuon$, Selection}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\begin{columns}
\column{0.2in}
{~}
\column{2in}
\ARROW Trigger
\begin{itemize}
\item Muon trigger.
\item Topological trigger.
\end{itemize}
\ARROW Good modelling with MC. \\
\ARROW Selection:
\begin{itemize}
\item As loose as possible.
\item Based on the $\PBzero$ vertex quality, impact parameters, loose Particle identification for the hadrons.
\item The variables were chosen in a way we are sure the are correctly modelled in MC.
\end{itemize}
\column{2.8in}
\includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_pt}.pdf}\\
\includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_costhetal}.pdf}
\end{columns}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Peaking backgrounds}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\ARROW A number of peaking backgrounds that can mistaken as your signal.\\
\ARROW There where a specially designed vetoes to fight each of them.
\begin{center}
\begin{tiny}
\hspace{-1cm}\begin{tabular}{ r | c c | c c }
\hline
& \multicolumn{2}{c|}{after preselection, before vetoes} & \multicolumn{2}{c }{after vetoes and selection}\\
Channel & Estimated events & \% signal & Estimated events & \% signal \\
\hline
\hline
$\PLambda_b \to \PLambda^{\ast}(1520)^{0} \mu\mu$ &$ (1.0\pm0.5)\times10^3 $&$ 19\pm8 $&$ 51\pm25 $&$ 1.0\pm0.4$\\
$\PLambda_b \to {\rm p } \PK \mu\mu$ &$ (1.0\pm0.5)\times10^2 $&$ 1.9\pm0.8 $&$ 5.7\pm2.8 $&$ 0.11\pm0.05$ \\
$\PBd \to \PKplus \mu \mu$ &$ 28\pm7 $&$ 0.55\pm0.06 $&$ 1.6\pm0.5 $&$ 0.031\pm0.006$\\
$\PBs \to \Pphi \mu \mu$ &$ (3.2\pm1.3)\times10^2 $&$ 6.2\pm2.1 $&$ 17\pm7 $&$ 0.33\pm0.12$\\
signal swaps &$ (3.6\pm0.9)\times10^2 $&$ 6.9\pm0.6 $&$ 33\pm9 $&$ 0.64\pm0.06$ \\
$\PBd \to \PKstar \PJpsi$ swaps &$ (1.3\pm0.4)\times10^2 $&$ 2.6\pm0.4 $&$ 2.7\pm2.8 $&$ 0.05\pm0.05$ \\
\hline
\end{tabular}
\end{tiny}
\includegraphics[angle=-90,width=0.49\textwidth]{{images/h_Bd_Kstmm_vetoes}.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{{h_Lb_L1520mm_vetoes}.pdf}
\end{center}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Multivariate selection}
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{0.55\textwidth}
\begin{itemize}
\item \href{http://arxiv.org/pdf/1512.04442v2.pdf}{{\color{blue}JHEP 1602 (2016) 104}}
\item PID, kinematics and isolation variables used in a Boosted Decision Tree (BDT) to reject background.
\item Reject the regions of $\PJpsi$ and $\Ppsi(2S)$.
\item Specific vetos for backgrounds: $\PLambdab \to \Pproton \PK \Pmu \Pmu$, $\PBs \to \Pphi \Pmu \Pmu$, etc.
\item Using k-Fold technique and signal proxy $\PB \to \PJpsi \PKstar$ for training the BDT.
\item Improved selection allowed for finer binning than the $1\invfb$ analysis.
\end{itemize}
\column{0.45\textwidth}
\includegraphics[angle=-90,width=0.88\textwidth]{images/Fig1.pdf} \\
\includegraphics[width=0.88\textwidth]{images/fold.png}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\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}{The columns of New Physics}
{~}
\begin{minipage}{\textwidth}
\begin{enumerate}
\item Maximum likelihood fit:
\begin{itemize}
\item The most standard way of obtaining the parameters.
\item Can have problem with low statistics.
\end{itemize}
\item Method of moments:
\begin{itemize}
\item Less precise then the likelihood estimator ($10-15\%$ larger uncertainties).
\item Does not suffer from the problems of likelihood fit.
\end{itemize}
\item Amplitude fit:
\begin{itemize}
\item Incorporates all the physical symmetries inside the amplitudes! The most precise estimator.
\item Has theoretical assumptions inside!
\end{itemize}
\end{enumerate}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Maximum likelihood fit - 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}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Maximum likelihood fit - Results}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[angle=-90,width=0.65\textwidth]{images/P5pPadOverlay.pdf}\\
\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 result; \href{http://arxiv.org/abs/1308.1707}{{ \color{blue}{Phys.Rev.Lett. 111 (2013) 191801}}}
\item SM: \href{http://arxiv.org/abs/1407.8526}{\color{blue}JHEP12(2014)125}
\end{itemize}
\end{minipage}
\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}{Method of moments - 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}
}
\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}
\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}{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}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
Other related LHCb measurements.
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PB \to \PKstar^{\pm} \Pmu \Pmu$}
{~}
\includegraphics[width=0.5\textwidth]{images/ksmumu_BF.png}
\includegraphics[width=0.5\textwidth]{images/kmumu_BF.png}
\begin{center}
\begin{columns}
\column{0.4\textwidth}
\begin{itemize}
\item Despite large theoretical errors the results are consistently smaller than SM prediction.
\item \href{http://arxiv.org/abs/1205.3422}{{ \color{blue}{JHEP 07 (2012) 133}}}
\end{itemize}
\column{0.6\textwidth}
\includegraphics[width=0.87\textwidth]{images/bukst_BF.png}
\end{columns}
\end{center}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PBs \to \Pphi \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.65\textwidth]{images/bs2phipi.png}\\
\end{center}
\begin{itemize}
\item Recent LHCb measurement \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}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PLambdab \to \PLambda \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\only<1>{
\includegraphics[width=0.65\textwidth]{images/Lb_BR.png}
}
\only<2>{
\includegraphics[width=0.45\textwidth]{images/Lblow.png}
\includegraphics[width=0.45\textwidth]{images/Lbhigh.png}
}
\end{center}
\begin{itemize}
\item 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}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Angular analysis of $\PLambdab \to \PLambda \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item For the bins in which we have $>3~\sigma$ significance the forward backward asymmetry for the hadronic and leptonic system.
\end{itemize}
\begin{center}
\includegraphics[width=0.9\textwidth]{{images/AFB_Lb}.png}
\end{center}
\begin{itemize}
\item $A_{FB}^H$ is in good agreement with SM.
\item $A_{FB}^{\ell}$ always in above SM prediction.
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{First observation of $\PBd \to \pi \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{3in}
\begin{itemize}
\item LHCb for the first time observed a CKM suppressed decay of $\PB \to \pi^{\pm} \Pmu \Pmu$
\item We observed $25 \pm 6$ events in $1~{ \rm fb }^{-1}$ data set.
\item Need to separate a large peaking component: $\PB \to \PK^{\pm} \Pmu \Pmu$ form our signal window.
\item In the future we can expect more aggressive physics program with this and similar channels $\mapsto$ see Kostas talk!
\end{itemize}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/pimumu.png}\\
\includegraphics[width=0.95\textwidth]{images/pimumu2.png}
\end{columns}
\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=0.9\textwidth]{images/uni2.png}
\item Challenging analysis due to bremsstrahlung.
\item Migration of events modeled by MC.
\item Correct for bremsstrahlung.
\item Take double ratio with $\PBplus \to \PJpsi \PKplus$ to cancel systematics.
\item In $3\invfb$, LHCb measures $R_K=0.745^{+0.090}_{-0.074}(stat.)^{+0.036}_{-0.036}(syst.)$
\item Consistent with SM at $2.6\sigma$.
\item See more details in Rafaels and Martinos talks!
\end{itemize}
\column{2.0in}
\includegraphics[width=0.99\textwidth]{images/RK.png}\\
\begin{itemize}
\item \href{http://arxiv.org/abs/1406.6482}{Phys. Rev. Lett. 113, 151601 (2014)}
\end{itemize}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Angular analysis of $\PBzero \to \PKstar \Pe \Pe$}
{~}
\begin{minipage}{\textwidth}
\only<1>{
\begin{itemize}
\item With the full data set ($3\invfb$) we performed angular analysis in $0.0004 < q^2 <1~\GeV^2$.
\item \href{http://arxiv.org/abs/1501.03038}{{\color{blue}{JHEP04(2015)064}}}
\end{itemize}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/Kstee2.png}\\
\end{center}
\begin{itemize}
\item Results in full agreement with the SM.
\item Similar strength on $C_7$ Wilson coefficient as from $\Pbeauty \to \Pstrange \Pphoton$ decays.
\end{itemize}
\iffalse
\begin{center}
\includegraphics[width=0.9\textwidth]{images/Kstee2.png}
\end{center}
\fi
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Steps in the near future}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item We are not there yet!
\item There might be something not taken into account in the theory.
\item Resonances ($\PJpsi$, $\Ppsi(2S)$) tails can mimic NP effects.
\item There might be some non factorizable QCD corrections.\\
'' However, the central value of this effect would have to be significantly larger than expected on the basis of existing estimates'' \texttt{D.Straub, 1503.06199}
.
\end{itemize}
\only<1>{
\includegraphics[width=0.9\textwidth]{images/charmloop.png}
}
\only<2>{
\begin{center}
\includegraphics[width=0.6\textwidth]{images/charmloop2.png}
\end{center}
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Conclusions}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item LHCb is and still will provide the most precise measurements of EWP!
\item Many analysis in the pipe line!
\item Even more ideas to what to do with existing and further data.
\end{itemize}
\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}{Angular analysis of $\PBzero \to \PKstar \Pe \Pe$}
{~}
\begin{minipage}{\textwidth}
\only<1>{
\begin{itemize}
\item With the full data set ($3\invfb$) we performed angular analysis in $0.0004 < q^2 <1~\GeV^2$.
\item \href{http://arxiv.org/abs/1501.03038}{{\color{blue}{JHEP04(2015)064}}}
\end{itemize}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/Kstee2.png}\\
\end{center}
\begin{itemize}
\item Results in full agreement with the SM.
\item Similar strength on $C_7$ Wilson coefficient as from $\Pbeauty \to \Pstrange \Pphoton$ decays.
\end{itemize}
\iffalse
\begin{center}
\includegraphics[width=0.9\textwidth]{images/Kstee2.png}
\end{center}
\fi
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Angular analysis of $\PBzero \to \PKstar \Pe \Pe$}
{~}
\only<1>{
\begin{minipage}{\textwidth}
\begin{itemize}
\item With the full data set ($3\invfb$) we performed angular analysis in $0.0004 < q^2 <1~\GeV^2$.
\item Electrons channels are extremely challenging experimentally:
\begin{itemize}
\item Bremsstrahlung.
\item Trigger efficiencies.
\end{itemize}
\item Determine the angular observables: $\FL$, $\ATD$, $\ATRe$, $\ATIm$:
\end{itemize}
\begin{equation}
\label{eq:physPars}
\begin{split}
\FL &=\frac{|A_0|^2}{|A_0|^2+|A_{||}|^2 + |A_\perp|^2}\\
\ATD &= \frac{|A_\perp|^2-|A_{||}|^2}{|A_\perp|^2+|A_{||}|^2}\\
\ATRe &= \frac{2\Real(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2}\\
\ATIm &= \frac{2\Imag(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2},
\end{split}\nonumber
\end{equation}
\end{minipage}
}
\only<2>{
\begin{center}
\includegraphics[width=0.5\textwidth]{images/Kstee.png}\\
\end{center}
\begin{itemize}
\item Results in full agreement with the SM.
\item Similar strength on $C_7$ Wilson coefficient as from $\Pbeauty \to \Pstrange \Pphoton$ decays.
\end{itemize}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/Kstee2.png}
\end{center}
}
\vspace*{2.1cm}
\end{frame}
\backupend
\end{document}
mchrzasz