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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Particle Phenomenology, Particle Astrophysics and Cosmology Seminar]{Particle Phenomenology, Particle Astrophysics and Cosmology Seminar}
\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}{0.9\textwidth}
\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Anomalies in Flavour Physics}
\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}
\end{column}
\end{columns}
\vspace{1em}
% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
\vspace{0.5em}
\textcolor{normal text.fg!50!Comment}{Imperial College \\October 16, 2015}
\end{center}
\end{frame}
}
\begin{frame}{Outline}
\begin{minipage}{\textwidth}
\begin{enumerate}
\item History of Flavour Physics discoveries.
\item
\item
\end{enumerate}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}{A lesson from history - GIM mechanism}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.62\textwidth]{images/GIM2.png}
\end{center}
\begin{columns}
\column{0.7\textwidth}
\begin{itemize}
\begin{footnotesize}
\item Cabibbo angle was successful at explaining dozens of decay rates in the 1960s.
\item There was one how ever that was not observed by experiments: $\PKzero \to \Pmuon \APmuon$.
\item Glashow, Iliopoulos, Maiani (GIM) mechanism was proposed in the 1970 to fix this problem. The mechanism required the existence of the $4^{th}$ quark.
\item At that point most of the people were skeptic about that. Fortunately in 1974 the discovery of the $\PJpsi$ meson silenced the skeptics.
\end{footnotesize}
\end{itemize}
\column{0.3\textwidth}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/GIM3.png}\\
\includegraphics[width=0.7\textwidth]{images/604.jpg}\\{~}\\{~}
\end{center}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{A lesson from history - CKM matrix}
\begin{minipage}{\textwidth}
\begin{center}
{~}\\{~}\\
\includegraphics[width=0.5\textwidth]{images/CKMmatrix.png}
\end{center}
\begin{columns}
\column{0.6\textwidth}
\begin{itemize}
\begin{small}
\item Similarly CP violation was discovered in 1960s in the neutral kaons decays.
\item $2 \times 2$ Cabbibo matrix could not allow for any CP violation.
\item For the CP violation to be possible one needs atleast $3 \times 3$ unitary matrix \\ $\looparrowright$ Cabibbo-Kobayashi-Maskawa matrix (1973).
\item It predicts existence of $\Pbottom$ (1977) and $\Ptop$ (1995) quarks.
\end{small}
\end{itemize}
\column{0.4\textwidth}
\begin{center}
{~}
%\includegraphics[height=2cm]{images/CP.png}\\
\includegraphics[width=0.96\textwidth]{bottom.jpg}
\end{center}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{A lesson from history - Weak neutral current}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[height=3cm]{images/weakcurr.png}{~}
\includegraphics[height=3cm]{images/weakcurr2.png}
\end{center}
\begin{columns}
\column{0.6\textwidth}
\begin{itemize}
\begin{small}
\item First the weak neutral currents were introduced in 1958 by Buldman.
\item Later on they were naturally build in unification of weak and electromagnetic interactions.
\item 't Hooft proved that the GWS models was renormalizable.
\item Everything was there in theory side, only missing piece was the experiment, till 1973.
\end{small}
\end{itemize}
\column{0.4\textwidth}
\begin{center}
{~}
%\includegraphics[height=2cm]{images/CP.png}\\
\includegraphics[width=0.85\textwidth]{images/bubblecern.png}
\end{center}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Modern challenges: loops come in to the game}
\begin{minipage}{\textwidth}
\begin{columns}
\column{0.5\textwidth}
\begin{itemize}
\item Standard Model contributions suppressed or absent:
\begin{itemize}
\item Flavour Changing Neutral Currents.
\item CP violation
\item Lepton Flavour/Number or Lepton Universality violation.
\end{itemize}
\item In general can probe physics beyond GPD reach.
\end{itemize}
\column{0.5\textwidth}
\includegraphics[width=0.99\textwidth]{{images/TauLFV_UL_2014001_averaged}.png}
\end{columns}
\begin{center}
\includegraphics[width=0.75\textwidth]{images/Bsmumu.png}
\includegraphics[width=0.20\textwidth]{{images/bsmumu_SM}.png}
\end{center}
\end{minipage}
\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}
$\color{JungleGreen}{\Rrightarrow}$ 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}}
}}
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)} }
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
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\begin{frame}{LHCb update of the $\PBzero \to \PKstar \Pmuon \APmuon$}
{~}
\begin{minipage}{\textwidth}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\backupbegin
\begin{frame}\frametitle{Backup}
\topline
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\end{document}
mchrzasz