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a/Seminars/ImperialCollege/mchrzasz.snm +++ b/Seminars/ImperialCollege/mchrzasz.snm @@ -0,0 +1 @@ +\beamer@slide {Js}{14} diff --git a/Seminars/ImperialCollege/mchrzasz.tex b/Seminars/ImperialCollege/mchrzasz.tex index 9378b85..18e11ac 100644 --- a/Seminars/ImperialCollege/mchrzasz.tex +++ b/Seminars/ImperialCollege/mchrzasz.tex @@ -186,7 +186,25 @@ \newcommand{\GeV}{\rm{GeV}} \newcommand{\MeV}{\rm{MeV}} \newcommand{\im}{\rm{Im}} +\newcommand{\invfb}{\rm{fb^{-1}}} \newcommand{\fixme}{\rm{{\color{red}{FIXME!}}}} +\newcommand{\thetal}{\theta_l} +\newcommand{\thetak}{\theta_k} +\newcommand{\nn}{\nonumber} +\newcommand{\eq}[1]{\begin{equation} #1 \end{equation}} +%\newcommand{\eqn}[1]{\begin{displaymath} #1 \end{displaymath}} +\newcommand{\eqa}[1]{\begin{eqnarray} #1 \end{eqnarray}} +\newcommand{\apeL}{{A_\perp^L}} +\newcommand{\apeR}{{A_\perp^R}} +\newcommand{\apeLR}{{A_\perp^{L,R}}} +\newcommand{\apaL}{{A_\|^L}} +\newcommand{\apaR}{{A_\|^R}} +\newcommand{\apaLR}{{A_\|^{L,R}}} +\newcommand{\azeL}{{A_0^L}} +\newcommand{\azeR}{{A_0^R}} +\newcommand{\azeLR}{{A_0^{L,R}}} + + \newcommand{\disp}{\displaystyle} \def\be{\begin{equation}} \def\ee{\end{equation}} @@ -401,7 +419,310 @@ \vspace*{2.1cm} \end{frame} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Recent measurements} +{~} +\only<1>{ + \begin{minipage}{\textwidth} + + +\begin{columns} + +\column{0.5\textwidth} +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Branching fractions:}} +\begin{description} +\item [$\PB^{0,\pm} \to \PK^{0,\pm} \Pmuon \APmuon$] {~}{~}LHCb, Mar 14 +\item [$\PB^{0} \to \PKstar \Pmuon \APmuon$] {~}{~}CMS, Jul 15 +\item [$\PBs \to \Pphi \Pmuon \APmuon$] {~}{~}{~}LHCb, Jun 15 +\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}LHCb, Sep 15 +\item [$\PLambdab \to \PLambda \Pmuon \APmuon$] {~}{~}{~}{~}LHCb, Mar 15 +\item [$\PB \to\Pmuon \APmuon$] {~}{~}{~}{~}{~}CMS+LHCb, Jun 15 +\end{description} + +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{CP asymmetry:}} +\begin{description} +\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}{~}LHCb, Sep 15 +\end{description} + +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Isospin asymmetry:}} +\begin{description} +\item [$\PB \to \PK \Pmuon \APmuon$] {~}{~}{~}{~}{~}LHCb, Mar 14 +\end{description} + + +\column{0.5\textwidth} +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Lepton Universality:}} +\begin{description} +\item [$\PB^{\pm} \to \PK^{\pm} \Plepton \APlepton$] {~}{~}LHCb, Jun 14 +\end{description} + + +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Angular:}} +\begin{description} +\item [$\PB^{0} \to \PK^{\ast} \Plepton \APlepton$] {~}{~}{~}LHCb, Jan 15 +\item [$\PB^{\pm} \to \PK^{\ast,\pm} \Plepton \APlepton$] BaBar, Aug 15 +\item [$\PBs \to \Pphi \Plepton \APlepton$] {~}{~}{~}LHCb, Jun 15 +\item [$\PLambdab \to \PLambda \Pmuon \APmuon$] {~}{~}LHCb, Mar 15 +\end{description} + + + + + +\end{columns} + +\end{minipage} +} +\only<2>{ + + \begin{minipage}{\textwidth} + + +\begin{columns} + +\column{0.5\textwidth} +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Branching fractions:}} +\begin{description} +\item [{\color{red}{$\PB^{0,\pm} \to \PK^{0,\pm} \Pmuon \APmuon$}}] {~}{~}{\color{red}{LHCb, Mar 14}} +\item [$\PB^{0} \to \PKstar \Pmuon \APmuon$] {~}{~}CMS, Jul 15 +\item [{\color{red}{$\PBs \to \Pphi \Pmuon \APmuon$}}] {~}{~}{~}{\color{red}{LHCb, Jun 15}} +\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}LHCb, Sep 15 +\item [$\PLambdab \to \PLambda \Pmuon \APmuon$] {~}{~}{~}{~}LHCb, Mar 15 +\item [{\color{red}{$\PB \to\Pmuon \APmuon$}}] {~}{~}{~}{~}{~}{\color{red}{CMS+LHCb, Jun 15}} +\end{description} + +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{CP asymmetry:}} +\begin{description} +\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}{~}LHCb, Sep 15 +\end{description} + +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Isospin asymmetry:}} +\begin{description} +\item [$\PB \to \PK \Pmuon \APmuon$] {~}{~}{~}{~}{~}LHCb, Mar 14 +\end{description} + + +\column{0.5\textwidth} +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Lepton Universality:}} +\begin{description} +\item [{\color{red}{$\PB^{\pm} \to \PK^{\pm} \Plepton \APlepton$}}] {~}{~}{\color{red}{LHCb, Jun 14}} +\end{description} + + +$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Angular:}} +\begin{description} +\item [{\color{red}{$\PB^{0} \to \PK^{\ast} \Plepton \APlepton$}}] {~}{~}{~}LHCb, Jan 15 +\item [{\color{red}{$\PB^{\pm} \to \PK^{\ast,\pm} \Plepton \APlepton$}}] {\color{red}{BaBar, Aug 15}} +\item [$\PBs \to \Pphi \Plepton \APlepton$] {~}{~}{~}LHCb, Jun 15 +\item [{\color{red}{$\PLambdab \to \PLambda \Pmuon \APmuon$}}] {~}{~}{\color{red}{LHCb, Mar 15}} +\end{description} + +\begin{alertblock}{} +$>2~\sigma$ deviations from SM + +\end{alertblock} + +\end{columns} + +\end{minipage} +} + + \vspace*{2.1cm} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%5 +\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$, where it all begun} +{~} + \begin{minipage}{\textwidth} +\only<1>{ +\begin{columns} +\column{0.6\textwidth} + August 2013:\\ + + \includegraphics[width=0.95\textwidth]{images/P5prime.png} +\column{0.4\textwidth} +\begin{itemize} +\item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data. +\item It turned out that the discrepancy occurred in an observable that was not constrained. + +\end{itemize} +\end{columns} + + +} + + + + +\only<2>{ + + +\begin{columns} +\column{0.6\textwidth} + August 2013:\\ + + \includegraphics[width=0.95\textwidth]{images/P5prime.png} +\column{0.4\textwidth} +\begin{itemize} +\item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data. +\item It turned out that the discrepancy occurred in an observable that was not constrained. + +\end{itemize} +\end{columns} + + +\begin{exampleblock}{} +Now let's move back and see the theory behind the $\PBzero \to \PKstar \Pmuon \APmuon$ and $P_5^{\prime}$. +\end{exampleblock} +} + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +\begin{frame}{Tools in rare $\PBzero$ decays} +{~} + \begin{minipage}{\textwidth} + +\begin{itemize} +\item \textbf{Operator Product Expansion and Effective Field Theory} +\end{itemize} +\begin{columns} +\column{0.1in}{~} +\column{3.2in} +\begin{footnotesize} + + +\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{footnotesize} +\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} +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{minipage} + \vspace*{2.1cm} +\end{frame} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$ kinematics} +{~} + \begin{minipage}{\textwidth} + +$\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decays is described in 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 $\PKstar$ ($\overline{\PKstar}$) rest frame and the direction of the $\PKstar$ ($\overline{\PKstar}$) 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=0.95\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[ +J_{1s} \sin^2\theta_K + J_{1c} \cos^2\theta_K + (J_{2s} \sin^2\theta_K + J_{2c} \cos^2\theta_K) \cos 2\theta_l\nn\\[1.5mm] +&&\hspace{-2.7cm}+ J_3 \sin^2\theta_K \sin^2\theta_l \cos 2\phi + J_4 \sin 2\theta_K \sin 2\theta_l \cos\phi + J_5 \sin 2\theta_K \sin\theta_l \cos\phi \nn\\[1.5mm] +&&\hspace{-2.7cm}+ (J_{6s} \sin^2\theta_K + {J_{6c} \cos^2\theta_K}) \cos\theta_l ++ J_7 \sin 2\theta_K \sin\theta_l \sin\phi + J_8 \sin 2\theta_K \sin 2\theta_l \sin\phi \nn\\[1.5mm] +&&\hspace{-2.7cm}+ J_9 \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,, +} +}} +$\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decays. + +} + +\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}} +}} + +\end{minipage} + \vspace*{2.1cm} +\end{frame} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Link to effective operators} +{~} + \begin{minipage}{\textwidth} + + + + + +\end{minipage} + \vspace*{2.1cm} +\end{frame} \backupbegin