\documentclass[xcolor=svgnames]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{polski}
%\usepackage{amssymb,amsmath}
%\usepackage[latin1]{inputenc}
%\usepackage{amsmath}
%\newcommand\abs[1]{\left|#1\right|}
\usepackage{amsmath}
\newcommand\abs[1]{\left|#1\right|}
\usepackage{hepnicenames}
\usepackage{hepunits}
\usepackage{color}
\usepackage{braket}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\definecolor{mygreen}{cmyk}{0.82,0.11,1,0.25}
%--------------------------------------------------------------------
% Introduction
%--------------------------------------------------------------------
\usetheme{Sybila}
\placelogotrue
\title[Recent BaBar results on CP violation in B-meson decays]{ Recent BaBar results on CP violation in B-meson decays}
\author{Marcin Chrz\k{a}szcz$^{1}$ \\ \footnotesize{on behalf of the BaBar collaboration}}
\institute{$^1$~University of Zurich \\{~}\\ Deep-Inelastic Scattering 2015 }
\date{\today}
\begin{document}
% --------------------------- SLIDE --------------------------------------------
\frame[plain]{\titlepage}
\author{Marcin Chrz\k{a}szcz}
% ------------------------------------------------------------------------------
% --------------------------- SLIDE --------------------------------------------
\institute{~(UZH)}
% --------------------------- SLIDE --------------------------------------------
\section{BaBar Detector}
\begin{frame}\frametitle{BaBar Detector}
\begin{columns}
\column{2.5in}
\begin{itemize}
\item PEP-II, an asymmetric $\Pelectron \APelectron$ collider.
\item Operating mostly at $\PUpsilon(4S)$ threshold.
\end{itemize}
\includegraphics[width=0.95\textwidth]{images/bbr_det.png}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/bbr_lumi.png}
\end{columns}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{frame}
\begin{frame}\frametitle{B factories}
\begin{columns}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/upsilon1.png}\\
\includegraphics[width=0.95\textwidth]{images/topo.png}
\column{2.5in}
\begin{itemize}
\item $\PB$ mesons produced in a clean environment.
\item Just above the $m(\PB \PB)$ threshold.
\end{itemize}
\includegraphics[width=0.95\textwidth]{images/ee_col.png}
\end{columns}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{frame}
\section{CP violation in $\PB \APB$ mixing}
\begin{frame}\frametitle{$\PBzero \APBzero$ mixing}
\begin{itemize}
\item Neutral mesons couple to their anti particles via weak interactions.
\end{itemize}
\begin{columns}
\column{3.4in}
\begin{itemize}
\item $\PBzero \Leftrightarrow \APBzero$, $\PBs \Leftrightarrow \APBs$, $\PK \Leftrightarrow \APK$.
\item We can writhe the weak eigenstates as:
\end{itemize}
\begin{equation*}
\ket{B_{L/H}} = \dfrac{1}{\sqrt{p^2+q^2}} (p \ket{\PBzero} \pm q \ket{\APBzero})
\end{equation*}
\begin{itemize}
\item Then the CP asymmetry can can be written as:
\end{itemize}
\begin{equation*}
A_{CP} = \dfrac{\mathcal{P}(\APBzero \to \PBzero) - \mathcal{P}(\PBzero \to \APBzero) }{\mathcal{P}(\APBzero \to \PBzero) + \mathcal{P}(\PBzero \to \APBzero)}\approx 2(1-|\frac{q}{p}|)
\end{equation*}
\column{1.5in}
\begin{center}
\includegraphics[width=0.99\textwidth]{images/Bmixing_dia.png}
\end{center}
\end{columns}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{itemize}
\item $\PUpsilon(4S)$ has an anti-symmetric state: $\dfrac{1}{\sqrt{2}} (\PBzero(t_1) \APBzero(t_2) - \APBzero(t_1) \PBzero(t_2))$
\item One $\PB$ is a specific flavour state tags the other one.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Inclusive dilepton measurement}
\begin{itemize}
\item $\PB$ mesons decay in $\sim 10\%$ semileptonicaly.
\item Charge of lepton determines the $\PB$ meson flavour.
\item If one observes same sign leptons $\to$ mixing occurred:
\end{itemize}
\begin{columns}
\column{0.5in}
{~}
\column{2.5in}
\begin{itemize}
\item $\Plepton^- \Plepton^{+}$: no mixing
\item $\Plepton^- \Plepton^{-}$: $\PBzero \to \APBzero$.
\item $\Plepton^+ \Plepton^{+}$: $\APBzero \to \PBzero$.
\end{itemize}
\column{2in}
\includegraphics[width=0.65\textwidth]{images/semillep.png}
\end{columns}
\begin{itemize}
\item Writing down the mixing provabilities~(time integrated):
\end{itemize}
\begin{equation*}
\mathcal{P}^{\pm \pm} \propto (1 \pm A_{CP}) \chi_d
\end{equation*}
\begin{equation*}
\mathcal{P}^{\pm \mp} \propto (1 -\chi_d)
\end{equation*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Detector effects}
\begin{footnotesize}
\begin{itemize}
\item Detector is not a perfect device $\to$ Introduced charge asymmetries $a_{\Plepton_j}$ for each $\Plepton_j$.
\item $\PUpsilon(4S)$ also goes to $\PBplus \PBminus$. Contribution: $r_B = N_{\PB^+ \PB^-}/N_{\PBzero \APBzero}$.
\item Time integrated probability gets modified:
\begin{align*}
\mathcal{P}^{\pm \pm} \propto (1 \pm a_{\Plepton_1} \pm a_{\Plepton_2} \pm A_{CP}) \chi_d \\
\mathcal{P}^{\pm \mp} \propto (1 -\chi_d + r_B)(1 \pm a_{\Plepton_1} \mp a_{\Plepton_2} )
\end{align*}
\item Summing over all events in $\Plepton_1 \Plepton_2 \in \lbrace \Pe \Pe, \Pe \Pmu, \Pmu \Pe, \Pmu \Pmu \rbrace$ categories:
\begin{align*}
N^{\pm \pm}_{\Plepton_1 \Plepton_2} = 1/2 N^0_{\Plepton_1 \Plepton_2} (1 \pm a_{\Plepton_1} \pm a_{\Plepton_2} \pm A_{CP}) \chi_d^{\Plepton_1 \Plepton_2}\\
N^{\pm \mp}_{\Plepton_1 \Plepton_2}= 1/2 N^0_{\Plepton_1 \Plepton_2} (1 -\chi_d^{\Plepton_1 \Plepton_2} + r_B)(1 \pm a_{\Plepton_1} \mp a_{\Plepton_2} )
\end{align*}
\item We got 16 observables, and 13 unknowns. $a_{\Plepton_j}$ highly correlated.
\item Adding events containing only single electron for $a_{\Pe}$ constrain.
\item 17 observables as input to $\chi^2$ fit, extracting: $A_{CP}$, 4 signal yields,\\ 4 efficiency asymmetries, 4 mixing probabilities.
\end{itemize}
\end{footnotesize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Systematics}
\begin{columns}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/table.png}
\column{2.3in}
\begin{itemize}
\item Dominant systematic from bias in MC.
\item Secondly the MC/data corrections to PID.
\item Difference in charge asymmetry between $\PBzero$ and average of $\PBzero$ and $\PB^{\pm}$.
\end{itemize}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Fit results}
\begin{center}
\begin{footnotesize}
\begin{tabular}{c c c c}
\hline \hline
\multicolumn{2}{c}{$A_{CP} = (-3.9 \pm 3.5)\times 10^{-3}$} & \multicolumn{2}{c}{ \includegraphics[height=0.5cm]{images/Babar_with_banner.jpg}~\href{http://arxiv.org/abs/1411.1842}{PRL 114, 081801 (2015)} }\\ \hline %\hline
$N^0_{\Pe\Pe}$ & $N^0_{\Pe\Pmu}$ & $N^0_{\Pmu\Pe}$ & $N^0_{\Pmu\Pmu}$ \\
$430875 \pm 515$ & $365343 \pm 429$ & $458200 \pm 480$ & $268077 \pm 381$ \\
$\chi_d^{\Pe\Pe}$ & $\chi_d^{\Pe\Pmu}$ & $\chi_d^{\Pmu\Pe}$ & $\chi_d^{\Pmu\Pmu}$ \\
$0.2248 \pm 0.0006$ & $0.1769 \pm 0.0006$ & $0.1754 \pm 0.0005$ & $0.2032 \pm 0.0007$ \\
$a^{\Pe 1}$ & $a^{\Pe 2}$ & $a^{\Pmu 1}$ & $a^{\Pmu 2}$ \\
$0.0034 \pm 0.0006$ & $0.0030 \pm 0.006$ & $-0.0056 \pm 0.0011$ & $-0.0065 \pm 0.0011$ \\ \hline
\end{tabular}
{~}\\
\begin{columns}
\column{0.5in}{~}
\column{2.5in}
\includegraphics[width=0.75\textwidth]{images/pull.png}
\begin{itemize}
\item Result $A_{CP} = (-3.9 \pm 3.5 \pm 1.9 )\times 10^{-3}$ in agreement with SM.
\end{itemize}
\column{2.5in}
\includegraphics[width=0.76\textwidth]{images/hfag.png}
\end{columns}
\end{footnotesize}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Flavour-changing neutral current}
\begin{itemize}
\item CKM structure in SM allows only the charged interactions to change flavour.
\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 by the GIM in SM $\to$~Rare decays.
\end{itemize}
\item LHCb already sees a $3.7~\sigma$ deviation in the angular observables in $\PBzero \to \PKstar \Pmuon \APmuon$. See my talk from yesterday: \href{https://indico.cern.ch/event/341292/session/15/contribution/40}{LINK}.
\item Here we present CP observables in $b \to s \Pphoton$ and $b \to s \Plepton \Plepton$ decays.
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Flavour-changing neutral current}
\begin{itemize}
\item CKM structure in SM allows only the charged interactions to change flavour.
\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 by the GIM in SM $\to$~Rare decays.
\end{itemize}
\item LHCb already sees a $3.7~\sigma$ deviation in the angular observables in $\PBzero \to \PKstar \Pmuon \APmuon$. See my talk LINK.
\item Here we present CP observables in $b \to s \Pphoton$ and $b \to s \Plepton \Plepton$ decays.
\end{itemize}
\end{frame}
\placelogofalse
\begin{frame}\frametitle{CP asymmetries in $\PB \to X_s \Pphoton$}
\begin{itemize}
\item Fully inclusive approach impossible.
\item Instead use semi-inclusive ( sum of exclusive modes).
\item 16 modes used (marked with $ \ast$)
\item Additional requirements:
\end{itemize}
\begin{columns}
\column{2in}
\begin{itemize}
\item \href{http://arxiv.org/abs/1406.0534}{PRD 90, 092001 (2014)}
\item Requirements:
\begin{itemize}
\item $m(X_s) \in (0.6,2.0)~\GeV$
\begin{itemize}
\item Indirect cut on $E_{\gamma} >2.3~\GeV$
\end{itemize}
\item $|\Delta E| <0.15~\GeV$
\item MVA based approach to get ride of $q\bar{q}$ background.
\end{itemize}
\end{itemize}
\column{3in}
\begin{tiny}
\begin{tabular}{l l | l l}
\hline
{~} & Final State & {~} &Final State\\
\hline
\hline
1* & $B^{+}\rightarrow K_{S}\pi^{+}\gamma$ & 20 & $B^{0}\rightarrow K_{S}\pi^{+}\pi^{-}\pi^{+}\pi^{-}\gamma$\\
2* & $B^{+}\rightarrow K^{+}\pi^{0}\gamma$ & 21 & $B^{0}\rightarrow K^{+}\pi^{+}\pi^{-}\pi^{-}\pi^{0}\gamma$\\
3* & $B^{0}\rightarrow K^{+}\pi^{-}\gamma$ & 22 & $B^{0}\rightarrow K_{S}\pi^{+}\pi^{-}\pi^{0}\pi^{0}\gamma$\\
4 & $B^{0}\rightarrow K_{S}\pi^{0}\gamma$ & 23* & $B^{+}\rightarrow K^{+}\eta\gamma$\\
5* & $B^{+}\rightarrow K^{+}\pi^{+}\pi^{-}\gamma$ & 24 & $B^{0}\rightarrow K_{S}\eta\gamma$\\
6* & $B^{+}\rightarrow K_{S}\pi^{+}\pi^{0}\gamma$ & 25 & $B^{+}\rightarrow K_{S}\eta\pi^{+}\gamma$\\
7* & $B^{+}\rightarrow K^{+}\pi^{0}\pi^{0}\gamma$ & 26 & $B^{+}\rightarrow K^{+}\eta\pi^{0}\gamma$\\
8 & $B^{0}\rightarrow K_{S}\pi^{+}\pi^{-}\gamma$ & 27* & $B^{0}\rightarrow K^{+}\eta\pi^{-}\gamma$\\
9* & $B^{0}\rightarrow K^{+}\pi^{-}\pi^{0}\gamma$ & 28 & $B^{0}\rightarrow K_{S}\eta\pi^{0}\gamma$\\
10 & $B^{0}\rightarrow K_{S}\pi^{0}\pi^{0}\gamma$ & 29 & $B^{+}\rightarrow K^{+}\eta\pi^{+}\pi^{-}\gamma$\\
11* & $B^{+}\rightarrow K_{S}\pi^{+}\pi^{-}\pi^{+}\gamma$ & 30 & $B^{+}\rightarrow K_{S}\eta\pi^{+}\pi^{0}\gamma$\\
12* & $B^{+}\rightarrow K^{+}\pi^{+}\pi^{-}\pi^{0}\gamma$ & 31 & $B^{0}\rightarrow K_{S}\eta\pi^{+}\pi^{-}\gamma$\\
13* & $B^{+}\rightarrow K_{S}\pi^{+}\pi^{0}\pi^{0}\gamma$ & 32 & $B^{0}\rightarrow K^{+}\eta\pi^{-}\pi^{0}\gamma$\\
14* & $B^{0}\rightarrow K^{+}\pi^{+}\pi^{-}\pi^{-}\gamma$ & 33* & $B^{+}\rightarrow K^{+}K^{-}K^{+}\gamma$\\
15 & $B^{0}\rightarrow K_{S}\pi^{0}\pi^{+}\pi^{-}\gamma$ & 34 & $B^{0}\rightarrow K^{+}K^{-}K_{S}\gamma$\\
16* & $B^{0}\rightarrow K^{+}\pi^{-}\pi^{0}\pi^{0}\gamma$ & 35 & $B^{+}\rightarrow K^{+}K^{-}K_{S}\pi^{+}\gamma$\\
17 & $B^{+}\rightarrow K^{+}\pi^{+}\pi^{-}\pi^{+}\pi^{-}\gamma$ & 36 & $B^{+}\rightarrow K^{+}K^{-}K^{+}\pi^{0}\gamma$\\
18 & $B^{+}\rightarrow K_{S}\pi^{+}\pi^{-}\pi^{+}\pi^{0}\gamma$ & 37* & $B^{0}\rightarrow K^{+}K^{-}K^{+}\pi^{-}\gamma$\\
19 & $B^{+}\rightarrow K^{+}\pi^{+}\pi^{-}\pi^{0}\pi^{0}\gamma$ & 38 & $B^{0}\rightarrow K^{+}K^{-}K_{S}\pi^{0}\gamma$\\
\hline
\end{tabular}
\end{tiny}
\end{columns}
\end{frame}
% \placelogotrue
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Asymmetry extraction}
\begin{itemize}
\item Asymmetry for fitted yields needs to be corrected as in previous analysis detector asymmetries.
\item Asymmetry extracted from side-bands.
\begin{itemize}
\item $(-1.4 \pm 0.7)~\%$.
\end{itemize}
\end{itemize}
\includegraphics[width=0.9\textwidth]{images/side.png}
\begin{columns}
\column{3in}
\begin{itemize}
\item Results:
\begin{itemize}
\item $A_{CP}(\PBplus \to X_s^+ \Pphoton) = (4.23 \pm 2.93 \pm 0.95)\%$
\item $A_{CP}(\PBzero \to X_s^0 \Pphoton) = (-0.74 \pm 2.57 \pm 1.10)\%$
\item Average:
\item $A_{CP} = (1.7 \pm 1.9 \pm 1.0)~\%$
\item SM: $A_{CP} \sim 0 \leftrightarrow Im(C_8) \sim 0$
\end{itemize}
\end{itemize}
\column{2in}
\includegraphics[width=0.9\textwidth]{images/im87.pdf}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{CP asymmetries in $\PB \to X_s \Plepton \Plepton$}
\begin{itemize}
\item Very important channel for NP searches.
\item Significant deviation found by LHCb.
\item CP observables are very clean predictions in SM and almost QCD free.
\item Similar ''semi-include'' modes: \begin{align*}
X_s= \lbrace \PK^+,~\PK^+\pi^0,~ \PK^+\pi^-,~\PK^+\pi^-\pi^0,\\ ~\PK^+\pi^-\pi^+,~\PK_s,~\PK_s\pi^+, ~\PK_s\pi^+\pi^0,~\PK_s\pi^+\pi^-\rbrace
\end{align*}
\item Look for two leptons flavours: $\Plepton \Plepton = \lbrace \Pe \Pe, \Pmu \Pmu \rbrace$
\item Additional requirements:
\begin{itemize}
\item Require: $m(X_s) < 1.8~\GeV$
\item $\Delta E \in [ -0.1 (-0.05), 0.05 ]$ for $\Plepton \Plepton = \Pe \Pe~( \Pmu \Pmu)$
\end{itemize}
\end{itemize}
\end{frame}
\placelogotrue
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Differential branching fraction}
\begin{columns}
\column{2.8in}
\begin{itemize}
\item \href{http://arxiv.org/abs/1312.5364}{PRL 112 (2014) 211802}
\item $\PJpsi,~(\Ppsi(2S))$ veto: $6.8-10.1~(12.9-14.2)~\GeV$
\item Suppress $q\bar{q}$ background with a BDT.
\item Perform a simultaneous fit to $m_{ES}$ and $L_R= \dfrac{\mathcal{P}_S}{\mathcal{P}_S+\mathcal{P}_B}$
\end{itemize}
\column{2.2in}
\includegraphics[width=0.9\textwidth]{images/ee_bin0.png}\\
\includegraphics[width=0.95\textwidth]{images/mumu_bin0.png}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{CP \& BR asymmetries results}
\begin{columns}
\column{2.5in}
\begin{footnotesize}
\begin{tabular}{|c|c|}
\hline
$q^2~[\GeV^2] $ & $A_{CP}$ \\ \hline \hline
$1.0 < q^{2} < 6.0$ & $-0.06 \pm 0.22 \pm 0.01$ \\ \hline
$0.1 < q^{2} < 2.0$ & $-0.13 \pm 0.18 \pm 0.01$ \\ \hline
$2.0 < q^{2} < 4.3$ & $\: 0.42 \: \: {}_{-0.42}^{+0.50} \pm 0.01$ \\ \hline
$4.3 < q^{2} < 6.8$ & $\! \! -0.45_{-0.57}^{+0.44} \pm 0.01$ \\ \hline
$10.1< q^{2} <14.2$ & $0.19 \: \: {}_{-0.17}^{+0.18} \pm 0.01$ \\ \hline
\end{tabular}
\begin{itemize}
\item Measured branching fractions($\times 10^{-6}$) :
\begin{equation*}
\mathcal{B}(\PB \to X_s \Pelectron \APelectron) = 7.69^{+0.82}_{-0.77}{}^{+0.50}_{-0.33} \pm 0.50
\end{equation*}
\begin{equation*}
\mathcal{B}(\PB \to X_s \Pelectron \APelectron) = 4.41^{+1.31}_{-1.17}{}^{+0.57}_{-0.42} \pm 0.27
\end{equation*}
\item Combined:
\begin{equation*}
\mathcal{B}(\PB \to X_s \Plepton^- \Plepton^+ ) = 6.73^{+0.70}_{-0.64}{}^{+0.34}_{-0.25} \pm 0.50
\end{equation*}
\item In agreement with SM.
\end{itemize}
\end{footnotesize}
\column{2.5in}
\includegraphics[width=0.9\textwidth]{images/results-q2.png}\\
\includegraphics[width=0.9\textwidth]{images/results-mx.png}
\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
\begin{frame}\frametitle{Conclusions}
\begin{enumerate}
\item B-factories still producing new results.
\item Presented new measurements of CP violation in neutral $\PB$ meson system using inclusive dileptons events.
\item BaBar continues to chase FCNC with measurement of CP asymmetries in: $b \to s \gamma$ and $b \to \Plepton \Plepton$
\item FCNC statistically limited: need future experiments.
\item All measurements consistent (for now?) with SM.
\end{enumerate}
\begin{center}
\includegraphics[width=0.45\textwidth]{images/digging-for-diamonds.png}
\end{center}
\end{frame}
\end{document}
mchrzasz