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\author{ {Marcin Chrzaszcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Search for massive neutrinos at LHCb and discovery potential of the FCC]{Search for massive neutrinos at LHCb and discovery potential of the FCC}
\date{21-27 August 2016}


\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 {Prospects and challenges for future ee and ep 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}\\
                  \includegraphics[width=0.7\textwidth]{fcclogo}
                  
                  \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]{uzh-transp}~~
\includegraphics[height=1.1cm]{ifj}

\end{column}
\end{columns}
 \textcolor{normal text.fg!30!Comment}{\begin{small}
 	Physik-Insitut, University of Zurich\\Instiute of Nuclear Physics, Polish Academy of Sciences
 \end{small}
}

\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!65!Comment}{Neutrinos at the High Energy Frontier, Amherst, 18-20 July, 2017}

	
\end{center}
\end{frame}
}

\iffalse
\section[Outline]{}
\begin{frame}
%\tableofcontents
%FIXME!
\begin{enumerate}
\item Rare $\PB$ decays:
\begin{itemize}
\item $\PB^+ \to \PK^+ \Ppi^- \Ppi^+ \Pphoton$
\item $\PBs/\PBzero \to \mu^- \mu^+$.
\item $\PBzero \to \PKstar \Pmuon \APmuon$.
\end{itemize}

\end{enumerate}

\end{frame}
\fi

%-------------------------------------------------------------------
%                          Introduction
%-------------------------------------------------------------------
%
% Set the background for the rest of the slides.
% Insert infoline
%\setbeamertemplate{background}
% {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}}
%\setbeamertemplate{footline}[bunsentheme]



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\setbeamertemplate{background}
% {\includegraphics[width=\paperwidth,height=\paperheight]{slide_bg}}
%\setbeamertemplate{footline}[bunsentheme]
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{LHCb detector}

%\begin{frame}\frametitle{LHCb detector}
%\begin{columns}
%\column{3.in}
%\begin{center}
%\includegraphics[width=0.98\textwidth]{det.jpg}
%\end{center}

%\column{2.0in}
%\begin{footnotesize}


 %     LHCb is a forward spectrometer:
 %       	\begin{itemize}
 %       	\item Excellent vertex resolution.
 %       	\item Efficient trigger.
 %       	\item High acceptance for $\Ptau$ and $\PB$.
 %       	\item Great Particle ID
 %       	\end{itemize}



%\end{footnotesize}
%\end{columns}

%\end{frame}

%\section{Introduction}
\iffalse
\begin{frame}\frametitle{Why long-lived particles?}
\begin{columns}
\column{3in}
\begin{itemize}
\item We all know here that the SM is incomplete.
\item Unfortunately we do no know what is the scale of NP.
\item NP can occur in the neutrino sector.
\item NP still can come from the Higgs sector $\Rightarrow$ not all properties are yet constrained.
\item There is a long list of theoretical models that predict the existence
of new particles that couple to the SM sector by mixing with the
Higgs.
\end{itemize}

\column{2in}
\includegraphics[width=0.9\textwidth]{susy/NP_couplings.png}


\end{columns}
\begin{itemize}

\item Inflaton, axion-like, dark matter mediator models also predict the
new boson to be light.
\item SUSY models also can have stable long living particles like $\Psquark$, $\Pslepton$.
\end{itemize}


\end{frame}

\fi

\begin{frame}\frametitle{Outline}

\ARROW Future $e^+ e^-$ colliders.\\
\begin{itemize}
\item ILC
\item CLIC
\item FCC{ee,eh}
\end{itemize}
\ARROW Detector\\
\ARROW Physics program:
\begin{itemize}
\item Higgs program.
\item Z pole program.
\item $\PW \PW$ program.
\item $t\bar{t}$ program.
\item Neutrino program.
\end{itemize}




\end{frame}


\begin{frame}\frametitle{Quo Vadis HEP?}

\begin{columns}
\column{0.5\textwidth}
What has LHC found...
\column{0.5\textwidth}
... and what is still missing.
\end{columns}

\begin{columns}
\column{0.5\textwidth}
\begin{columns}
\column{0.02\textwidth}
{~}
\column{0.4\textwidth}
\includegraphics[width=0.95\textwidth]{images/HiggsBoson.jpg}
\column{0.55\textwidth}
\begin{small}
\ARROW A Higgs boson.\\
~~~ $m_H=125~\GeV$\\
~~~ $\Gamma_H=4.1~\MeV$
\end{small}
\end{columns}

\column{0.5\textwidth}
\begin{columns}
\column{0.02\textwidth}
{~}
\column{0.4\textwidth}
\includegraphics[width=0.95\textwidth]{{images/mystery-box_21582}.jpg}
\column{0.55\textwidth}
\begin{footnotesize}
\ARROW Dark matter/energy?\\
\ARROW Neutrino masses?\\
\ARROW Matter/antimatter asymmetry?
\end{footnotesize}
\end{columns}

\end{columns}
{~}\\
\ARROW LHC has ongoing physics program...\\\vspace{0.5cm}
\begin{columns}
\column{0.5\textwidth}
\ARROWorange Run 2 +3: $300~$ by 2023
\column{0.5\textwidth}
\ARROWorange HL-HLC: $3000$ by 2035
\end{columns}

\begin{columns}
\column{0.75\textwidth}
\ARROW But what for post-LHC area? Need to plan now!\vspace{0.5cm}
\includegraphics[width=0.9\textwidth]{images/future.jpg}

\column{0.25\textwidth}
\includegraphics[width=0.9\textwidth]{images/close1.jpg}

\end{columns}


%\textref{Int. J. Mod. Phys. A30 (2015) 1530022}
%\vspace*{2.1cm}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{International Linear Collider (ILC)}
\includegraphics[width=0.99\textwidth]{images/ilc.png}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{International Linear Collider (ILC)}
\begin{footnotesize}
\ARROW The ILC concept was reviewed by the Japanese government.
\begin{columns}
\column{0.5\textwidth}
\begin{alertblock}{Feedbacks (domestic only)}
\ARROW Academia in general:\\
reserved/hostile\\
\ARROW Funding authorities:\\
reserved/critical\\
\ARROW Political allies (Local/Central):\\
enthusiastic/cautious
\end{alertblock}

\column{0.5\textwidth}
\ARROW ``Given the fact that the energy scale of new physics is currently unknown,
the physics reach of precision Higgs and other SM probes of ILC250
are comparable to that of ILC500'', Hiroaki Aihara

\end{columns}


\end{footnotesize}
\vspace{0.5cm}
\includegraphics[width=0.9\textwidth]{images/ilc2.png}


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Compact Linear Collider (CLIC)}
\begin{footnotesize}
\ARROW CLIC also wants a staged approach:\vspace{0.5cm}
\begin{columns}
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/clic.png}

\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/clic2.png}


\end{columns}

\includegraphics[width=0.95\textwidth]{images/clicl2.png}
\end{footnotesize}





\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Future Circular Collider (FCC)}

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

\begin{exampleblock}{FCC - study:}
\ARROWR $pp$ collider: the ultimate goal.\\
\ARROWR $ee$ collider: first step.\\
\ARROWR $ep$ collider: additional option.\\ \vspace{1.cm}

\ARROWorange $98~\rm km$ infrastructure in Geneva area\\
\vspace{0.7cm}
\ARROWR The Goal: CDR and cost review by the end of 2018!
\end{exampleblock}

\column{0.5\textwidth}
\includegraphics[width=0.99\textwidth]{images/fcc.png}

\end{columns}



\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}%\frametitle{Future Circular Collider (FCC)}
\fullsizegraphic{images/cdr.png}
\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Time line of FCC}
\includegraphics[width=0.95\textwidth]{images/time.png}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Why circular collider?}
\begin{columns}
\column{0.7\textwidth}
\begin{block}{}
\ARROW To achieve interesting physics program one would have to obtain a factor of $10^3$ of LEP luminosity.\\
\ARROW The Luminosity scales:
\begin{equation}
L \sim R \frac{P_{SR}}{\beta^{\ast}} \nonumber
\end{equation}


\end{block}
\column{0.3\textwidth}
\includegraphics[width=0.9\textwidth]{images/dino.jpg}
\end{columns}\vspace{0.5cm}


\ARROW So how can one increase the luminosity without the electric energy cost?\\
\begin{columns}
\column{0.7\textwidth}

\ARROW The answer is inside the B-factory design!\\
\ARROW One has to lower the beam emittance: $\beta^{\ast}$.
\column{0.3\textwidth}
\only<2>{
\includegraphics[width=0.9\textwidth]{images/dino2.jpg}
}
\end{columns}\vspace{0.5cm}

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\beta^{\ast}$ over last 40 years}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/betas.png}

\end{center}

\ARROW The $\beta^{\ast}$ will be increased to $1\rm mm$ compared to $5~\rm cm$ at LEP.\\
\ARROW SuperKEKB will pave the way towards $\beta^{\ast} < 1~\rm mm$.\\
\ARROW Additional improvements to reach the $10^3$ factor in lumi are:
\begin{itemize}
\item Continues injection
\item More bunches
\end{itemize}

\end{frame}








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Beam parameters}
\begin{center}
\includegraphics[width=0.99\textwidth]{images/beam.png}
\end{center}
\vspace{0.5cm}
\ARROW Identical beam optics for all energies.\\
\ARROW FCC would have two separate rings\\
\ARROW Detectors similar to the ILC and CLIC.


\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Comparison of $e^+ e^-$ colliders}

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

\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{FCCep}
\begin{columns}
\column{0.7\textwidth}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/FCCep.png}
\end{center}

\column{0.3\textwidth}
\ARROW Requires additional ERL\\
\ARROW Would be needed anyway for FCChh.

\end{columns}

\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Detectors requirements}
\begin{center}
\includegraphics[width=1.03\textwidth]{images/det1.png}
\end{center}
\textref{E.Leogrande}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{CLIC detector}
\begin{center}
\includegraphics[width=1.03\textwidth]{images/det2.png}
\end{center}
\textref{E.Leogrande}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Tracker}
\begin{center}
\includegraphics[width=1.03\textwidth]{images/det3.png}
\end{center}
\textref{E.Leogrande}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{IDEA detector}
\begin{center}
\includegraphics[width=1.03\textwidth]{images/det4.png}
\end{center}
\textref{M.Dam}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Tracker}
\begin{center}
\includegraphics[width=1.03\textwidth]{images/det5.png}
\end{center}
\textref{M.Dam}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Tracker (for) the idea ;)}
\begin{center}
\includegraphics[width=1.03\textwidth]{images/det6.png}
\end{center}
\textref{M.Dam}
\end{frame}








%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
Physics program
\end{Huge}
\end{center}
\end{frame}









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Higgs production}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/higgs.png}
\end{center}
\end{frame}









%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Higgs Mass}

\ARROW A very clean Higgs mass determination in $e^+ e^- \to \PZ \PH$ and using a recoil technique (unique for lepton colliders):
\begin{equation}
m_{\rm recoil}= (\sqrt{s} - E_{\mu})^2 - \vert p_{\mu} \vert^2 \nonumber
\end{equation}
\ARROW With $\PZ \to \mu \mu$ and $\PZ \to e e$\\
\ARROW $\PZ \PH$ decays are tagged independently of the Higgs decay mode.\\
\begin{center}
\begin{columns}
\column{0.5\textwidth}
\ARROW Precise measurement of $g_{HZZ}$:
\includegraphics[width=0.75\textwidth]{images/higgsStrau.png}

\column{0.5\textwidth}
\includegraphics[width=0.9\textwidth]{images/ZH.png}


\end{columns}
\end{center}


\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Higgs Width}
\ARROW Higgs-strahlung.\vspace{0.3cm}
\begin{columns}
\column{0.3\textwidth}
\includegraphics[width=0.75\textwidth]{images/higgsStrau.png}

\column{0.7\textwidth}
\ARROW Total HZ crossection: \\
$\sigma(HZ) \propto g^2_{HZZ}$\\
\ARROW Exclusive cross section:\\
$\sigma(HZ) \times Br(H\to XX) \propto g^2_{HZZ} \frac{g^2_{HXX}}{\Gamma_H}$


\end{columns}
\vspace{0.5cm}

\ARROW Total Higgs width from $\PW\PW$ process:

\begin{columns}
\column{0.3\textwidth}
\includegraphics[width=0.85\textwidth]{images/higgsV.png}

\column{0.7\textwidth}
\begin{equation}
\frac{\sigma(HZ) \times Br(H\to b \bar{b})}{\sigma(H\nu \nu) \times Br(H\to b \bar{b})} \propto \frac{g_{HZZ}^2}{g_{HWW}^2} \nonumber
\end{equation}
\ARROW And finally:
\begin{align*}
\sigma(H\nu\nu) \times Br(H \to \PW \PW^{\ast} ) \propto \frac{g^4_{HWW}}{\Delta_H}
\end{align*}
\ARROWorange From this: $\Delta_H$.

\end{columns}
\textref{Credit to Mark Thomson}
\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Higgs Couplings}
\ARROWR The Higgs couplings to $\PW\PW$, $\PZ\PZ$, $c\bar{c}$, $gg$, $\tau^-\tau^+$, $\gamma\gamma$ can be determined via tagging the respective Higgs decay final states\\

\begin{columns}
\column{0.5\textwidth}
\ARROW Observables: \vspace{0.1cm}
\begin{align*}
\sigma(e^+e^- \to ZH) \times Br(H \to X)
\end{align*}
\begin{align*}
\sigma(e^+e^- \to H\nu \nu) \times Br(H \to X)
\end{align*}

\includegraphics[width=0.7\textwidth]{images/plot.png}


\column{0.5\textwidth}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/table.png}
\end{center}


\end{columns}
\ARROWR Factor of $10$ improvements for most couplings.


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Higgs Production in S-channel}
\ARROW Potentially possibility to measure the $\PH ee$ Yukawa coupling!\\
\begin{columns}

\column{0.6\textwidth}
\ARROW Several final states can be studied.\\
\ARROW It requires running:
\begin{align*}
\sqrt{s}=M_H=125~\GeV
\end{align*}
\ARROW Since $\Gamma_{\PH}=4.2~\MeV$, it requires monochromatization (increasing the energy resolution in the CMS energies for $\Pe^- \Pe^+$ interaction without reducing the inherent                 energy spread of the colliding beams)\vspace{0.3cm}

\includegraphics[width=0.85\textwidth]{images/table2.png}


\column{0.4\textwidth}
\includegraphics[width=0.75\textwidth]{images/Hee.png}\\ \vspace{0.2cm}
\includegraphics[width=0.85\textwidth]{images/Hee2.png}


\end{columns}
\ARROWorange Limits 3.5 times the SM predictions in both cases.

 \end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Normalized Higgs Couplings}

\ARROW Higgs couplings normalized to the SM predictions:
\begin{columns}
\column{0.65\textwidth}
\begin{align*}
k_x = \frac{g_{\PH xx}}{g^{SM}_{\PH xx}}
\end{align*}
\includegraphics[width=0.95\textwidth]{images/kx.png}


\column{0.35\textwidth}
\includegraphics[width=0.95\textwidth]{images/kx2.png}


\end{columns}



\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{MegaTop: $t\bar{t}$ threshold scan}

\begin{columns}
\column{0.4\textwidth}

\ARROW For the first time the the top quark to be studied using a precisely defined leptonic state.\\
\ARROW The dependence of the t quark cross-section shape on the t quark mass and interactions is computable to high precision (depends on $m_t$, $\Gamma_t$, $\alpha_s$, $g_Htt$, ISR, luminosity spectrum).\\

\column{0.6\textwidth}
\includegraphics[width=0.9\textwidth]{images/mt.png}

\end{columns}


\begin{columns}


\column{0.75\textwidth}
\includegraphics[width=0.99\textwidth]{images/mt2.png}

\column{0.25\textwidth}

\ARROW PRD: 
\begin{align*}
m_=(173.21 \pm 0.51 \pm 0.71)~\GeV
\end{align*}

\ARROW FCCee: 
\begin{align*}
\sigma(m_t)<10~\MeV
\end{align*}

\end{columns}









\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Physics program $\PW \PW$}
\ARROW Measurement of $m_W$ from $\sigma_{\PW\PW}$
\begin{columns}

\column{0.6\textwidth}
\includegraphics[width=0.95\textwidth]{images/mW.png}
\ARROWR Max statistical sensitivity at $\sqrt{s}=2m_W+0.6~\GeV$
\column{0.4\textwidth}
\begin{exampleblock}{Stat. precision}
\ARROWorange with $L=11~\rm pb^{-1} \rightarrow~350~\MeV$
\ARROWorange with $L=8~\rm ab^{-1} \rightarrow~0.4~\MeV$

\end{exampleblock}

\begin{alertblock}{Sys. precision needed:}
\ARROWorange $\Delta E(\rm beam)$ $<0.4~\MeV$\\
\ARROWorange $\Delta \epsilon / \epsilon <10^{-4}$\\
\ARROWorange $\Delta \sigma_B <0.7~\rm fb$
\end{alertblock}







\end{columns}
\begin{center}
\begin{align*}
\Delta m_W^{FCC} = 500~\keV~~~~~~~~~~~\Delta m_W^{LEP} = 50~\MeV
\end{align*}

\end{center}



\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Physics program at the $\PZ$ pole}

\ARROW $L=3 \times 10^{36}$ $\rightarrow$ $4 \times 10^{12}$ Z decays. \\
\ARROW $\PZ$ mass and width wit precision of $10~\keV$ (stat) $+100~\keV$ (sys).\\
\begin{columns}
\column{0.4\textwidth}
\includegraphics[width=0.95\textwidth]{images/Z.png}
\column{0.6\textwidth}
\ARROW Radiation function calculated to $\mathcal{O}(\alpha_s^3) \sim 10^{-4}$\\ \vspace{0.15cm}
\ARROW Relative	precisions (\href{https://link.springer.com/article/10.1007/JHEP01(2014)164}{JHEP01(2014)164}):\\
~~\ARROWorange $R_{\ell} = \frac{\Gamma_{\ell}}{\Gamma_{\rm had}} \sim 5 \times 10^{-5}$\\
~~\ARROWorange $R_{b} = \frac{\Gamma_{b\bar{b}}}{\Gamma_{\rm had}} \sim 2-5 \times 10^{-5}$\\
~~\ARROWorange $N_{\nu} \sim 10^{-3}$
\end{columns}

\begin{columns}
\column{0.5\textwidth}
\begin{align*}
\Delta_{\rm rel} \alpha_s(m^2_Z) \sim 2 \times 10^{-3}
\end{align*}

\column{0.5\textwidth}
\begin{align*}
\Delta_{\rm QED} \alpha_s(m^2_Z) \sim 3 \times 10^{-3}
\end{align*}

\end{columns}


\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\PZ$ asymmetries}
\ARROW $\PZ$	boson	decay	to	$ff$: 3	observables	from the direction and decay of the	outgoing fermion.

\begin{columns}
\column{0.35\textwidth}
\begin{align*}
A_f = \frac{2g_{Vf}g_{Af}}{ g^2_{Vf} + g^2_{Af}}
\end{align*}

\begin{align*}
\sin^2 \theta^{\ell}_{eff} = \frac{1}{4}\left( 1- \frac{g_{V\ell}}{g_{A\ell}} \right)
\end{align*}

\column{0.65\textwidth}
\ARROW With $e$, $\mu$, $\tau$, $c$ and $b$ one can measure:
\begin{align*}
A_{FB} = \frac{\sigma_F - \sigma_B}{\sigma_{tot}} = \frac{3}{4} A_e A_f
\end{align*}
\ARROW With $\tau$:
\begin{align*}
A_{pol} = \frac{\sigma_{F,R} + \sigma_{B,R}  - \sigma_{F,L} - \sigma_{B,L}  }{\sigma_{tot}} = -A_f
\end{align*}
\begin{align*}
A^{FB}_{pol} = \frac{\sigma_{F,R} - \sigma_{B,R}  - \sigma_{F,L} + \sigma_{B,L}  }{\sigma_{tot}} = - \frac{3}{4} A_e
\end{align*}


\end{columns}
\ARROWR With polarized beams we have two additional asymmetries:
\begin{align*}
A_{LR}= \frac{\sigma_{l} - \sigma_r}{\sigma_{tot}}=A_e~~~~~~A^{FB}_{pol} = \frac{\sigma_{F,l} - \sigma_{B,l}  - \sigma_{F,r} + \sigma_{B,r}  }{\sigma_{tot}} = - \frac{3}{4} A_f
\end{align*}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{$\PZ$ pole summary}

\begin{center}
\includegraphics[width=1.0\textwidth]{images/Z2.png}
\end{center}



\textref{From A.Blondel}
\end{frame}







%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Flavour Physics}
\ARROW Flavour Physics is an very active topic:
\begin{center}
\begin{columns}
\column{0.6\textwidth}
\ARROW LHCb will dominate in the decays where the muon are in final state.\\
\ARROW However $\tau$s are very challenging for them!
\includegraphics[width=0.95\textwidth]{images/Kstartautau.png}\vspace{0.2cm}
\ARROW Overall $\mathcal{O}(10^3)$ events!\\
\ARROW Angular analysis possible.\\
\ARROW Similar beeing studied for $\PBs \to \tau \tau$.


\column{0.4\textwidth}

\includegraphics[width=0.97\textwidth]{images/P5prime2.png}\\
\includegraphics[width=0.75\textwidth]{images/RKstar.png}\\
\includegraphics[width=0.75\textwidth]{images/RK2.png}

\end{columns}





\end{center}
\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Right-handed neutrinos}

\begin{center}
\includegraphics[width=0.9\textwidth]{images/nu.png}
\end{center}
\ARROWR Neutrino oscillations: at least two massive light neutrinos.
\ARROWR No renormalisable way in the SM therefore $\rightarrow$ evidence for new physics.
\ARROWR Sterile neutrinos for type I seesaw mechanism.

\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{ Neutrino mass eigenstates}
\ARROW See-saw mechanism:

\begin{center}
\begin{align*}
\mathcal{L}=\frac{1}{2} (\bar{\nu}_L , \bar{N}^e_R ) \begin{pmatrix}
0 & m_D \\
m_D^T & M_R
\end{pmatrix}
\begin{pmatrix}
v^c_L \\
N_R
\end{pmatrix}
\end{align*}
\begin{alertblock}{}
$\tan 2 \theta = \frac{2m_D}{M_R}$,~~~$m_{\nu}=\frac{1}{2} \left[ M_R - \sqrt{M^2_R +4m^2_D} \right]$\\
$M=\frac{1}{2} \left[ M_R + \sqrt{M^2_R +4m^2_D} \right]$\\

\end{alertblock}
\begin{footnotesize}
\begin{columns}
\column{0.32\textwidth}
\begin{block}{Dirac only}
$M_R=0$, $m_D \neq 0$\\
\ARROWR 4 states of equal masses.\\
\ARROW $I=1/2$ active neutrinos.\\
\ARROW $I=0$ sterile neutrinos.
\end{block}

\column{0.32\textwidth}
\begin{alertblock}{Majorana only}
$M_R \neq 0$, $m_D = 0$\\
\ARROW 4 states of equal masses.\\
\ARROW $I=1/2$ active neutrinos.\\
\ARROW $I=0$ sterile neutrinos.
\end{alertblock}

\column{0.32\textwidth}
\begin{exampleblock}{Dirac + Majorana}
$M_R \neq 0$, $m_D \neq 0$\\
\ARROWR 4 states of diff. masses.\\
\ARROWR $I=1/2$ active neutrinos.\\
\ARROWR $I=0$ ALMOST sterile neutrinos.\\

\end{exampleblock}




\end{columns}



\end{footnotesize}
\end{center}





\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{ Right handed neutrinos}

\begin{columns}
\column{0.5\textwidth}
\begin{align*}
\nu= \nu_L \cos \theta  - N_R^c \sin \theta
\end{align*}
\begin{align*}
N= N_R \cos \theta  + \nu_L^c \sin \theta
\end{align*}

\column{0.5\textwidth}
\begin{block}{}
$\nu_L$  - light mass eigenstate\\
$N$ - heavy mass eigenstate\\
$\nu_L$ - active neutrino\\
$N_R$ - ``sterile'' neutrino
\end{block}


\end{columns}\vspace{0.1cm}
\ARROWR In the EW interaction the $\nu_L$ are produced:
\begin{align*}
\nu_L = \nu  \cos \theta + N \sin \theta
\end{align*}
\ARROW Many consequences:\\
\ARROWorange  Effect on neutrino oscillations ($\eV$ mass)\\
\ARROWorange Dark matter ($\keV$ mass regime)\\
\ARROWorange $\PZ$ invisible width.\\
\ARROWorange Exotic particle decays: $\PH \nu N$ and $\PZ \nu N$.\\
\ARROWorange Heavy Flavour physics: strange, charm, beauty flavoured mesons via $\PW^{\ast}$.\\
\ARROWorange Violation on lepton flavour/universality.


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Collider experiments}
\begin{columns}
\column{0.5\textwidth}
\ARROWR B-factories:
\includegraphics[width=0.9\textwidth]{images/B-Majorana2.pdf}

\column{0.5\textwidth}
\ARROWR $pp$ colliders:
\includegraphics[width=0.9\textwidth]{images/nu3.jpg}




\end{columns}

\begin{columns}
\column{0.5\textwidth}
\ARROWR Z factory:
\includegraphics[width=0.9\textwidth]{images/nu4.png}

\column{0.5\textwidth}
\ARROWR $ee$ colliders:
\includegraphics[width=0.9\textwidth]{images/nu5.png}\\
and many many more...

\end{columns}
\textref{arxiv::1503.05491}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Production in Z decays}
\ARROW Production:
\begin{align*}
Br(\PZ \to \nu_m \bar{\nu} ) = Br(\PZ \to \nu \bar{nu}) \vert U \vert^2 \left(1-\frac{m^2_{\nu_m}}{m^2_Z} \right)^2 \left(1+ \frac{1}{2}\frac{m^2_{\nu_{m}}}{m^2_Z}  \right)
\end{align*}
\begin{alertblock}{}
\begin{columns}
\column{0.4\textwidth}
~~\ARROW Decay length:
\begin{align*}
L \approx \frac{3 {\rm cm}}{\vert U \vert^2 (m^2_{\nu})^6 }
\end{align*}
\column{0.6\textwidth}
\includegraphics[width=0.85\textwidth]{images/nu6.png}



\end{columns}

\end{alertblock}
\ARROW Background: four fermion: $e^- e^+ \to \PW^{\ast}  \PW^{\ast} $, $e^- e^+ \to \PZ^{\ast}(\nu\nu) +\PZ/\gamma$\\
\ARROW Long lifetime of $N$ helps rejecting the background!


\textref{A.Blendel}
\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Detection at a hadron collider}
\begin{columns}
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/HNLv.png}
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/eventdisplay2.png}

\end{columns}

\ARROW Super easy to detect topology!\\
\ARROW At least two charged tracks produced.


\end{frame}

\begin{frame}\frametitle{Signatures at FCCs}


\begin{center}
\includegraphics[width=0.75\textwidth]{images/nu10.png}
\end{center}
\ARROW FCCee:
\begin{itemize}
\item Displaced vertices (Z-pole).
\item Electroweak precision measurements (mostly Z-pole).
\item Higgs boson production and decay modes.
\end{itemize}
\ARROW FCC-hh/e: LFV, LNV, displeased vertex.


\textref{arxiv::1612.02728}
\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Current picture}

\begin{center}
\includegraphics[width=0.9\textwidth]{images/nu9.png}
\end{center}

\ARROW Present limits are dominated by LEP.\\
\ARROW Higgs decays: Best constraints from $\PH\to \gamma \gamma$


\textref{JHEP 1505 (2015) 053}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Sensitivity}
\ARROW Preliminary studies show excellent potential!\\
\ARROW Confirmation needed, based on accurate detector simulation\\
\ARROW Complementarity with other CERN projects (e.g., SHiP, see N.Serra talk tmr.)

\begin{center}
\includegraphics[width=0.99\textwidth]{images/nu7.png}
\end{center}


\textref{arxiv:1411.5230v2}
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Synergy between FCC-xy}
\ARROW Systematics assessment of heavy neutrino signatures at colliders.\\
\ARROW First looks FCC-hh and FCC-he sensitivities.\\
\ARROW Golden channels:
\begin{itemize}
\item FCC-hh: LFV signatures and displeased vertexes.
\item FCC-he LFV signatures and displeased vertexes.
\item FCC-hh: EWPO and displeased vertexes.

\end{itemize}

\begin{center}
\includegraphics[width=0.9\textwidth]{images/nu8.png}
\end{center}
\textref{O.Fischer}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Summary}
\ARROW The FCC program is constantly growing.\\
\ARROW CDR in 2018!\\
\ARROW One of the core program of FCC are HNL!\\
\ARROW future colliders will exclude large part of parameter space!
\begin{center}
\includegraphics[width=0.7\textwidth]{images/Joke.jpg}                                                                                                        
\end{center}

\end{frame}









\backupbegin

\begin{frame}\frametitle{Backup}


\end{frame}




\backupend

\end{document}
