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\def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace}
\def\ARROWR{{\color{WildStrawberry}{$\Rrightarrow$}}\xspace}

\author{ {Marcin Chrzaszcz} (CERN, IFJ)}
\institute{CERN, IFJ}
\title[Searches for heavy neutral leptons at the Future Circular Colliders]{Searches for heavy neutral leptons at the Future Circular Colliders}


\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}{0.75\textwidth}                                                                         
                        \flushright\bfseries \LARGE {Searches for heavy neutral leptons at the Future Circular Colliders }                                              
                \end{column}                                                                                           
                \begin{column}{0.02\textwidth}                                                                         
                  {~}                                                                                                  
                  \end{column}                                                                                         
                \begin{column}{0.23\textwidth}                                                                         
                 % \hspace*{-1.cm}                                                                                     
                  \vspace*{-3mm}                                                                                       
                  \includegraphics[width=0.6\textwidth]{lhcb-logo}                                                     
                  \end{column}                                                                                         
                                                                                                                       
        \end{columns}                                                                                                  
\end{center}                                                                                                           
        \quad                                                                                                          
        \vspace{3em}                                                                                                   
\begin{columns}                                                                                                        
\begin{column}{0.44\textwidth}                                                                                         
\flushright \vspace{-1.8em} { \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}{on behalf of the FCC collaboration,\\ CERN and \\ Institute of Nuclear Physics, Polish Academy of Science}\normalsize\\                                                              
\vspace{0.5em}                                                                                                         
                                                                                                                       
        \textcolor{normal text.fg!50!Comment}{15th Rencontres du Vietnam,\\ Quy Nhon, 4-10 August 2019}                                          
\end{center}                                                                                                           
\end{frame}                                                                                                            
}                                  



\begin{frame}\frametitle{Particles of SM}

\begin{center}
\begin{columns}

\column{0.45\textwidth}
\includegraphics[width=0.99\textwidth]{SM.png}

\column{0.55\textwidth}

\pause
\ARROW In the SM neutrinos do not appear in the right-handed state.\\
\ARROW By construction neutrino are massless.\\
\ARROWR Neutrino oscillations are evidence for physics beyond the SM!
\includegraphics[width=0.99\textwidth]{neutrino-mix.jpg}
\end{columns}

\end{center}


\end{frame}


\begin{frame}\frametitle{Extending the SM}


\ARROW A lazy person solution is to add the right-handed neutrinos in:
\includegraphics[width=0.95\textwidth]{nuMSM.jpg}\\
\pause
\ARROW But where are they?


\hfill arXiv::hep-ph/0605047, M.Shaposhnikov

\end{frame}

\begin{frame}\frametitle{Seesaw mechanism}


\begin{columns}


\column{0.5\textwidth}

\begin{align*}
~~\mathcal{L} = \mathcal{L}_{SM}+\bar{\ell_L}F \nu_R \epsilon \Phi^*- \frac{1}{2}\bar{\nu_R^c} M_M \nu_R + \rm H.c.
\end{align*}
~~\ARROW After the EWSB:
\begin{align*}
~~\frac{1}{2} \left( \bar{\nu_L} \bar{\nu^{c}_R } \right) \mathcal{M} \left( \nu_{L}^c \nu_R  \right)^T
\end{align*}



\column{0.5\textwidth}

\includegraphics[width=0.95\textwidth]{Seesaw_mechanism_Header.png}


\end{columns}
\ARROW In the vanilla seesaw:
\begin{align*}
\mathcal{M} = \begin{pmatrix} 
0 & M_D \\
M_D & M_M
\end{pmatrix}~~~~~\Rightarrow \lambda_+ \sim M_D ,~~~ \lambda_- \sim - \frac{M_M^2}{M_D }
\end{align*}
\pause
\ARROW In reality:
\begin{align*}
\mathcal{M}=\begin{pmatrix}{\delta}m_{\nu}^{1loop} & M_D \\ M_D^T & M_M + {\delta}M_N^{1loop} \end{pmatrix}
\end{align*}



\end{frame}

\begin{frame}\frametitle{Seesaw mechanism}



\ARROW Diagonalization matrix:
\begin{align*}
\mathcal{U}= \begin{pmatrix} \cos(\theta) & \sin(\theta) \\ -\sin(\theta^\dagger) & \cos(\theta^\dagger)  \end{pmatrix}
\begin{pmatrix} U_{\nu} & \\ & U_N^{\ast} \end{pmatrix}
\end{align*}

\begin{align*}
\mathcal{U}^{\dagger}\mathcal{M}\mathcal{U}^{\ast}=\begin{pmatrix}m_{\nu}^{\rm diag} & \\ & M_N^{\rm diag} \end{pmatrix}
\end{align*}
with 
\begin{align*}
M_N^{\rm diag}&=U_N^T M_N U_N=\text{diag}(M_1,M_2,M_3)\label{MNdiagDef}\\
m_{\nu}^{\rm diag}&= U_{\nu}^{\dagger}m_{\nu}U_{\nu}^{\ast}=\text{diag}(m_1,m_2,m_3). 
\end{align*}
\ARROW For small mixings:
\begin{equation*}
\mathcal{U}=\Bigg[ \begin{pmatrix} \mathbb{I}-\frac{1}{2}\theta\theta^{\dagger} & \theta \\ -\theta^{\dagger} & \mathbb{I}-\frac{1}{2}\theta^{\dagger}\theta \end{pmatrix} + \mathcal{O}(\theta^3) \Bigg]\begin{pmatrix} U_{\nu} & \\ & U_N^{\ast} \end{pmatrix},
\end{equation*}





\end{frame}




\begin{frame}\frametitle{Correction to SM processes}


\ARROW Charge currents:
\begin{align*}
j_{\mu}^+=\frac{g}{2}{\color{blue}{\theta_{\alpha}}}\bar{ell}_{\alpha}\gamma_{\mu}N
\end{align*}
\ARROW Neutral currents:
\begin{align*}
j_{\mu}^0= \nu_{\alpha}\gamma_{\mu} {\color{blue}{\theta_{\alpha}}} N
\end{align*}
\ARROW The Yukawa couplings:
\begin{align*}
\mathcal{L}_{Yukawa}=\mathcal{L}^{SM}_{Yukawa}{\color{blue}{\theta_{\alpha}}}
\end{align*}

\end{frame}




\begin{frame}\frametitle{Current status}


\ARROW Since the RHN are modifying fundamental properties of SM they are hugely constrained:




\begin{columns}
\column{0.5\textwidth}


\begin{alertblock}{Indirect}
\begin{itemize}
\item EW precision observables
\item LFV, LNV
\item Neutrinoless double beta decay
\item Big Bang Nucleosynthesis

\end{itemize}
\end{alertblock}

\pause
\column{0.5\textwidth}


\begin{exampleblock}{Direct}
\begin{itemize}
\item Beam dump searches
\item Collider searches (LEP, LHC, etc.)
\end{itemize}
\end{exampleblock}


\end{columns}




\end{frame}




\begin{frame}\frametitle{Current status}

\includegraphics[width=0.45\textwidth]{{M_Ue_capped}.pdf}
\includegraphics[width=0.45\textwidth]{{M_Umu_capped}.pdf}


\ARROW \footnotesize M.C., M. Drewers, T. Gonzalo, J. Harz, S. Krishnamurthy, C. Weniger, arXiv::1908:XYZZ

\end{frame}



\begin{frame}\frametitle{Where the constrains come from?}
\begin{center}
\includegraphics[width=0.7\textwidth]{{M_Ue_limits}.pdf}

\end{center}
\ARROW The direct searches are the strongest constraints where production cross sections are the largest.\\
\ARROW \footnotesize arXiv::1908:XYZZ


\end{frame}


\begin{frame}\frametitle{Indirect constraints}
\ARROW The indirect searches show power for high couplings:
\begin{center}
\includegraphics[width=0.49\textwidth]{{M_Utau_CKM_Zinv_Rtau}.pdf}
\includegraphics[width=0.49\textwidth]{{Utau_lnL_highmass}.pdf}
\end{center}
\ARROW Small excess is visible. Consistent with the fluctuation.\\
\ARROW \footnotesize arXiv::1908:XYZZ
\end{frame}




\begin{frame}\frametitle{}

\begin{center}
What can happen in the future?

\begin{center}
\only<1>{
\includegraphics[width=0.8\textwidth]{crystall.jpg}
}

\only<2>{
\includegraphics[width=0.8\textwidth]{crystall2.jpg}
}
\end{center}
\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{FCCee in context}
\begin{columns}
\column{0.65\textwidth}
\includegraphics[width=0.99\textwidth]{lumi.jpg}\\
\ARROW Check out the CDR : CERN-ACC-2018-0057\\
\ARROW Also the theory report: arXiv:1905.05078 
\column{0.35\textwidth}
\ARROW The FCCee is the most efficient machine up to the $\Ptop\APtop$ threshold.\\
\includegraphics[width=0.99\textwidth]{CDR.jpg}


\end{columns}
\end{frame}




\begin{frame}\frametitle{Schematizing sterile neutrino searches at FCC}

\begin{center}
\includegraphics[width=0.99\textwidth]{coupling.png}
\end{center}

\footnotesize
\hfill Credit to S.Antusch, E.Cazzato, O.Fischer, arXiv::1612.02728

\end{frame}


\begin{frame}\frametitle{Displaced vertexes}

\begin{center}
\includegraphics[width=0.99\textwidth]{fcceh.jpg}
\end{center}
\ARROW In the interesting region: $m<m_W$ and $\theta < 10^{-5}$ \\
\ARROW Displacement: measurement of primary (production) vertex.\\
\ARROW Secondary vertex with ,,large'' displacement\\
\ARROWR ee  he: A few times tracking resolution: $\mathcal{O}(10)\rm \mu m$,\\
\ARROWR hh: Beyond background, detector noise, pileup: $\mathcal{O}(10) \rm cm$.\\
\hfill Credit to S.Antusch, E.Cazzato, O.Fischer, arXiv::1612.02728

\end{frame}



\begin{frame}\frametitle{FCCee direct}

\begin{center}
\includegraphics[width=0.7\textwidth]{fccee.jpg} 

\end{center}
\footnotesize arXiv::1710.03744, S.Antuscha, E.Cazzato, M.Drewes, O.Fischer,B.Garbrecht, D.Gueterb, J.Klari
\end{frame}


\begin{frame}\frametitle{FCCee indirect}

\begin{center}
\includegraphics[width=0.95\textwidth]{indirect.jpg}
\end{center}
\ARROW Modification of the theory prediction of precision observables.\\
\ARROW Also CKM unitarity, cLFV, LUV.\\
\ARROW Currently still dominated by LEP!

\end{frame}

\begin{frame}\frametitle{FCCee Higgs portal}

\begin{center}
\includegraphics[width=0.95\textwidth]{higgs.jpg}
\end{center}
\ARROW Mono-Higgs production mechanism!\\
\ARROW New Higgs decays:
\begin{itemize}
\item Modification of Higgs Branching fractions.
\item New decays: $\PHiggs \to N \nu$.
\item Invisible width modification.
\end{itemize}
\ARROW Modification of triple Higgs coupling.

\end{frame}


\begin{frame}\frametitle{FCCeh}

\begin{center}
\includegraphics[width=0.75\textwidth]{FCCeh.jpg}
\end{center}
\ARROW Large Lorentz boost makes the displaced vertexes clearly visible.\\
\ARROW Many final states to look at:\\
\includegraphics[width=0.49\textwidth]{Wq.jpg}
\includegraphics[width=0.49\textwidth]{Wgamma.jpg}


\hfill Credit to S.Antusch, E.Cazzato, O.Fischer, arXiv::1612.02728

\end{frame}

\begin{frame}\frametitle{FCChh}

\begin{center}
\includegraphics[width=0.75\textwidth]{FCChh.jpg}
\end{center}
\ARROW LFV is the thing to look for!!!\\
\ARROW The best final states: $\ell^{\pm}_{\alpha}\ell^{\mp}_{\beta} j j$, $\ell^{\pm} \ell^{\mp} \ell^{\pm}_{\gamma}$\\
\ARROW For ep machine the more sensitive ones are: $\mu jjj$ and $\tau jjj$.\\
\ARROW Also LNU are there: $\mu ^{\pm}\mu^{\pm} j$ (pp) and $e^{+} j$ (ep).



\end{frame}

\begin{frame}\frametitle{FCC in total}
\begin{columns}

\column{0.5\textwidth}
\begin{center}
\includegraphics[width=0.99\textwidth]{total.jpg}
\end{center}

\column{0.5\textwidth}


\ARROW FCCee:
\begin{itemize}
\item Dominates the exclusion below the $m_W$ mass.
\item Precision indirect constraints: EWPO, CKM, etc.
\end{itemize}
\ARROW FCCeh, FCChh:
\begin{itemize}
\item Sensitivity in high mass region.
\item Higgs potential.
\item LFV, LNV.
\end{itemize}

\end{columns}
\hfill Credit to S.Antusch, E.Cazzato, O.Fischer, arXiv::1612.02728



\end{frame}




\begin{frame}\frametitle{Summary}
\ARROW Hunting for RHN is very well motivated.\\
\ARROW Neutrino program has to be considered a core of future colliders.\\
\ARROW FCC has unique sensitivity for RHN!\\
\ARROW Huge amount of measurements and constraints to be performed.\\
\ARROW Complementarity between different colliders.\\
\begin{center}
\begin{block}{Credit to M. Drewers, arXiv::1903.06100}
\includegraphics[width=0.7\textwidth]{summary.png}
\end{block}
\end{center}

\end{frame}



\backupbegin

\begin{frame}\frametitle{Backup}
\topline

\end{frame}





\backupend

\end{document}
