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\author{ {Marcin Chrzaszcz} (IFJ PAN)}
\institute{UZH}
\title[LFV and LUV at FCCee]{LFV and LUV at FCCee}


\begin{document}
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{
\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 \huge {Lepton Flavor and Universality Violation at FCCee}
		\end{column}
                \begin{column}{0.02\textwidth}
                  {~}
                  \end{column}
                \begin{column}{0.23\textwidth}
                 % \hspace*{-1.cm}
                  \vspace*{-3mm}
                  \includegraphics[width=0.7\textwidth]{fcc}
                  \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 Chrzaszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}          
                                                                                                                                                               
\end{column}                                                                                                                                                   
\begin{column}{0.53\textwidth}                                                                                                                                 
%\includegraphics[height=1.3cm]{cern}{~}{~}                                                                                                                    
~~~~\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, D. Gorbunov}\normalsize\\
\vspace{0.5em}

	\textcolor{normal text.fg!50!Comment}{Snowmass, 28$^{th}$ September 2020}
\end{center}
\end{frame}
}


{\vspace{5.4cm}
\usebackgroundtemplate{\includegraphics[width=0.98\paperwidth]{FCC.jpg}}%
\begin{frame}\frametitle{FCC}



\end{frame}
}

{\vspace{5.4cm}
\usebackgroundtemplate{\includegraphics[width=0.98\paperwidth]{FCC2.jpg}}%
\begin{frame}\frametitle{FCC}



\end{frame}
}
{
\usebackgroundtemplate{\includegraphics[width=0.98\paperwidth]{physics.jpg}}%
\begin{frame}\frametitle{FCCee Physics}


\end{frame}
}





\begin{frame}\frametitle{The European Strategy}

\begin{columns}

\column{0.6\textwidth}
\begin{block}{~}
\begin{center}

\includegraphics[width=0.99\textwidth]{images/strategy3.png}\\
\includegraphics[width=0.99\textwidth]{images/strategy2.png}

\end{center}
\end{block}

\column{0.4\textwidth}

\begin{center}
\includegraphics[width=0.95\textwidth]{images/strategy.png}
\end{center}
\end{columns}


\end{frame}



\begin{frame}\frametitle{Lepton Flavour/Number Violation}                                                              
\begin{small}                                                                                                          
 Lepton Flavour Violation(LFV):                                                                                        
\end{small}                                                                                                            
                                                                                                                       
                                                                                                                       
\begin{footnotesize}                                                                                                   
                                                                                                                       
After $\Pmuon$ was discovered it was natural to think of it as an excited $\Pelectron$.                                
\begin{columns}                                                                                                        
\column{3in}                                                                                                           
\begin{itemize}                                                                                                        
\item Expected: $B(\mu\to\Pe\gamma) \approx  10^{-4}$                                                                  
\item Unless another $\Pnu$, in intermediate vector boson loop, cancels.                                               
\end{itemize}                                                                                                          
                                                                                                                       
\column{2in}                                                                                                           
{~}\includegraphics[width=0.98\textwidth]{rabi.png}                                                                    
                                                                                                                       
\end{columns}                                                                                                          
\begin{columns}                                                                                                        
\column{0.5in}                                                                                                         
{~}                                                                                                                    
\column{3in}                                                                                                           
\begin{block}{I.I.Rabi:}                                                                                               
"Who ordered that?"                                                                                                    
\end{block}                                                                                                            
\column{0.3in}{~}                                                                                                      
\column{2in}                                                                                                           
{~}\includegraphics[scale=0.08]{II_Rabi.jpg}                                                                           
                                                                                                                       
\end{columns}                                                                                                          
                                                                                                                       
                                                                                                                       
\begin{itemize}                                                                                                        
\item Up to this day charged LFV is being searched for in various decay modes.                                         
\item LFV was already found in neutrino sector (oscillations).                                                         
\end{itemize}                                                                                                          
\end{footnotesize}                                                                                                     
                                                                                                                       
                                                                                                                       
\begin{footnotesize}                                                                                                   
                                                                                                                       
\begin{columns}                                                                                                        
\column{3.5in}                                                                                                         
\begin{small}                                                                                                          
 Lepton Number Violation (LNV)                                                                                         
\end{small}                                                                                                            
                                                                                                                       
\begin{itemize}                                                                                                        
\item Even with LFV, lepton number can be a conserved quantity.                                                        
\item Many NP models predict it violation(Majorana neutrinos)                                                          
\item Searched in so called Neutrinoless double $\beta$ decays.                                                        
\end{itemize}             


\column{1.5in}                                                                                                         
\includegraphics[width=0.8\textwidth]{Double_beta_decay_feynman.png}                                                   
                                                                                                                       
\end{columns}                                                                                                          
                                                                                                                       
\end{footnotesize}                                                                                                     
%Double_beta_decay_feynman.png                                                                                         
                                                                                                                       
  % \textref{M.Chrz\k{a}szcz 2014}                                                                                     
\end{frame}                                                                                                            
              


                                                                                                                       
\begin{frame}\frametitle{Lepton Universality}                                                                          
\ARROW What is Lepton Universality?                                                                                    
\begin{center}                                                                                                         
\includegraphics[width=0.95\textwidth]{images/LUV.png}                                                                 
\end{center}                                                                                                           
\pause                                                                                                                 
\ARROW Or mathematically speaking:                                                                                     
\begin{equation}                                                                                                       
\mathcal{L}_f=\bar{f} i D_{\mu}\gamma^{\mu}f,~~f=l^i_L \nonumber                                                       
\end{equation}                                                                                                         
\begin{equation}                                                                                                       
D_{\mu}=\partial_{\mu} + i \frac{{\color{red}{g}}}{2} \sigma_j W_{\mu}^j \nonumber                                     
\end{equation}                                                                                                         
                                                                                                                       
\ARROW Basic property of SM!                                                                                           
\end{frame}                                                                                                            
            




                                                                                                                       
\begin{frame}\frametitle{Lepton Universality Violation}                                                                          



\begin{columns}

\column{0.5\textwidth}
\ARROW Charge currents:\\
$R(\PDstar) = \frac{\Br (\PB \to \PDstar \tau \nu )}{\Br(\PB \to \PDstar \mu \nu)}  $
{~}\\


\includegraphics[width=0.7\textwidth]{rdrds_spring2019.png}                                                            


\ARROW Discrepancy reduced to $3.1~\sigma$.\\                                                                          
\ARROW Theoretical uncertainties are still  negligible.\\                                                              




\column{0.5\textwidth}

\ARROW FC Neutral currents:\\

$R_{\PK/\PKstar} = \frac{\Br(\PB \to \PK/\PKstar \mu \mu)}{\Br(\PB \to \PK/\PKstar e e)}$\\{~}\\
\only<1>{
\includegraphics[angle=-90,width=0.65\textwidth]{images/RK2019.pdf}\\                                                  


\begin{align*}                                                                                                         
 R_K = 0.846^{+0.060}_{-0.054}  ({\rm stat.}) ^{+0.016}_{-0.014}({\rm syst})
\end{align*} 

\ARROW $2.5~\sigma$ deviation from SM.
}
\only<2>{

\includegraphics[width=0.65\textwidth]{images/Fig10a.pdf}\\                                                  

\begin{align*}                                                                                                         
R_{\PKstar}^{\rm low~q^2} = 0.66^{+0.11}_{-0.07}  ({\rm stat.}) \pm 0.03({\rm syst})\\
R_{\PKstar}^{\rm mid~q^2} = 0.69^{+0.11}_{-0.07}  ({\rm stat.}) \pm 0.05({\rm syst})
\end{align*}  


}
\end{columns}

\end{frame}                                                                                                            
            
\begin{frame}\frametitle{Expected data}
\begin{columns}
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/lumi2.png}\\                                                  

\ARROW Huge luminosity compared to other projects. \\
\ARROW Especially in the ''lower'' energy spectrum.\\


\column{0.5\textwidth}

\begin{exampleblock}{Amount of Bosons produced}
\ARROWR $\PZ$: $5 \times 10^{12}$ \\
\ARROWR $\PW\PW:$ $10^{8}$\\
\ARROWR $\PZ\PH$: $10^{6}$\\
\ARROWR $\Ptop\APtop$: $10^{6}$
\end{exampleblock}

\includegraphics[width=0.95\textwidth]{images/lumi.png}\\                                                  



\end{columns}
\end{frame}

\begin{frame}\frametitle{LFV at $\PZ$}
\ARROW Testing anomalous couplings of the $\PZ$ boson:
\begin{itemize}
\item $\PZ \to \ell \ell^{\prime}$
\end{itemize} 
\includegraphics[width=0.95\textwidth]{images/pdg.png}\\                                                  

\begin{columns}
\column{0.5\textwidth}
\ARROW Currently the measurements are in range $10^{-5} - 10^{-6}$, dominated by LEP and ATLAS experiments.

\column{0.5\textwidth}
\ARROW With $5\times 10^{12}$ $\PZ$ decays the FCC is expected to probe region of $\mathcal{O}(10^{-9})$.


\end{columns}
\end{frame}

\begin{frame}\frametitle{LFV at $\PZ$, RHN}
\ARROW Huge amount of $\PZ$ means also huge amount of neutrinos!\\
\ARROW Can test the Right Handed Neutrino Model:
\begin{itemize}
\item $\PZ \to \nu_{R} \bar{\nu}$
\item $\nu_R \to \nu \PZ^{\ast}$, $\PZ^{\ast} \to \nu\bar{\nu}/ \ell \bar{\ell}/q\bar{q}$
\item $\nu_R \to \ell \PW^{\ast}$, $\PW^{\ast} \to \nu \ell/q\bar{q}^{\prime}$
\end{itemize}
\begin{columns}
\column{0.35\textwidth}
\ARROW Possible to probe the mass of RHN in range $\left[0.5,80\right]~\rm GeV/c^2$\\
Credit to M. Drewers


\column{0.6\textwidth}
\includegraphics[width=0.95\textwidth]{images/summary.png}\\                                                  

\end{columns}



\end{frame}




\begin{frame}\frametitle{LFV with heavy flavours}

\ARROW The $\PZ$ runs is also a Flavour factory:
\begin{center}
\includegraphics[width=0.95\textwidth]{images/HFP.png}
\end{center}
\begin{columns}
\column{0.45\textwidth}
\begin{alertblock}{$\tau \to \ell \gamma$}
\ARROW Sensitivity $2\times 10^{-9}$.\\
\ARROW Compatible with Belle II.\\
\ARROW Background dominated.
\end{alertblock}


\column{0.5\textwidth}
\begin{exampleblock}{$\tau \to \ell \ell \ell$}
\ARROWR Sensitivity $1 \times 10^{-10}$.\\
\ARROWR Factor of 2 better then Belle II.\\
\ARROWR Background free.
\end{exampleblock}




\end{columns}


\end{frame}



\begin{frame}\frametitle{Lepton Universality with heavy flavors}

\begin{alertblock}{~}
\ARROW LU is essentially a test of coupling constant of charge currents.\\
\ARROW The easiest is to measure: $\frac{g_{\mu}}{g_{e}}$.\\
\ARROW This can be obtained using partial width: $\tau \to \mu \nu \nu$ and $\tau \to e \nu \nu$. Known to $0.14~\%$ precision. \\
\end{alertblock}


\begin{exampleblock}{~}
\ARROWR The ratios $\frac{g_{\tau}}{g_{e}}$ and $\frac{g_{\tau}}{g_{\mu}}$ require the measurements:
\begin{itemize}
\item $\tau \to \mu \nu \nu$ or $\tau \to e \nu \nu$.
\item $\mu \to e \nu \nu$.
\end{itemize}
\end{exampleblock}
\ARROW FCCee aims to improve these measurements with an order of magnitude!!!



\end{frame}



\begin{frame}\frametitle{Lepton Universality with heavy flavors}
\begin{columns}

\column{0.5\textwidth}
\ARROW FCCee can shade the light on the LUV anomalies.\\
\ARROW We expect over 1000 events of $\PB \to \PKstar \tau\tau$.\\
\ARROWR Allows to measure the angular observables, but also to test LUV:
\begin{align*}
R_{\PKstar}^{\tau/\ell}=\frac{\Br(\PB \to \PK/\PKstar \tau \tau)}{\Br(\PB \to \PK/\PKstar \ell \ell)}
\end{align*}
\ARROW 
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/kstartautau.png}

\end{columns}
\ARROW Can achieve precision of $5\%$ for $R_{\PKstar}^{\tau/\ell}$.\\
\ARROW Allows to measure the LUV in angular observables.\\
\ARROW More of the $b \to s$ transitions with $\tau$ leptons will have similar sensitivities!

\end{frame}













\begin{frame}\frametitle{Conclusions}

\ARROW FCCee after the recent European Strategy Update the FCC is progressing towards TDR.\\
\ARROW Thanks to the Tera $\PZ$ run the FCCee is electroweak and flavor factory.\\
\ARROW Measurements of LFV and LUV parameters will complement other B-factories ($b \to s$ transitions), and in most cases be the most precise measurements to date.\\
\ARROW Check out the FCC:
\begin{columns}
\column{0.5\textwidth}
\ARROW Visit our web page and sign up for updates:\\
\href{https://fcc-ee.web.cern.ch/}{\url{https://fcc-ee.web.cern.ch/}}
\column{0.5\textwidth}
\begin{exampleblock}{Referneces}
\ARROWR FCC Physics Opportunities, CERN-ACC-2018-0056\\
\ARROWR 	FCC-ee: The Lepton Collide, CERN-ACC-2018-0057\\
\ARROWR And others: 1906.02693, 1809.01830, 1506.00918  
\end{exampleblock}

\end{columns}


\end{frame}







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