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\author{\sf Athanasios Dedes}
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%%%%%%%%%%local defs
\def\hl{h}
\def\ha{A}
\def\hh{H}
\def\hpm{H^\pm}
\def\mha{m_{\ha}}
\def\mhl{m_{\hl}}
\def\mhh{m_{\hh}}
\def\amu{\delta a_\mu^{\rm NP}}
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\def\ifmath#1{\relax\ifmmode #1\else $#1$\fi}
\def\ls#1{\ifmath{_{\lower1.5pt\hbox{$\scriptstyle #1$}}}}
%%%%%%%%%%%%%%%%
\newcommand{\dam}{\delta a_\mu^{\rm SUSY}}
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\newcommand{\mev}{\mbox{MeV}}
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%
\newcommand{\bc}{\begin{center}}
\newcommand{\ec}{\end{center}}
\newcommand{\spa}{\vspace{0.5cm}}
\renewcommand{\bs}{$B_s\rightarrow\mu^+\mu^-$}
\newcommand{\cbs}{{\cal B}(B_s\rightarrow\mu^+\mu^-)}
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\begin{document}
\parskip=3mm
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\lhead{}
\rhead{\sf  \thepage}
\headrulewidth 2pt
\footrulewidth 2pt
\chead{\sf{\usebox{\Title}}}
\date{30/6/2000}
\def\diad#1{\def\diadvalue{#1}}\def\diadvalue{}
\diad{\sf University of Bonn}
\lfoot{\diadvalue}
%\cfoot{\mbox{\epsfxsize=2.3cm\epsfysize=2.3cm
%\epsffile{../ral/ppd.ps}}}
%
% \begin{tabular}{cc}
%   \mbox{\epsfxsize=1.3cm\epsfysize=1.3cm\epsffile{clrc.ps}} &
%   \mbox{\epsfxsize=1.3cm\epsfysize=1.3cm\epsffile{EPS/CERN.eps}}  \\
% \end{tabular}


\Trtitle{\sf $B_s \to \mu^+\mu^-$ and Trilepton  Events  at the
Tevatron   }
%
\Large
\sf
%
\begin{titlepage}


\setlength{\fboxrule}{2pt}

\vskip1cm

\begin{center}
%{\LARGE \Red{  Across the Present Energy Frontier : Probing the Origin
% of mass,
% \\ Corfu, Greece, 10 - 12 September 2001}}\\[0.4cm]
%                           Collider Physics          }} \\
%{\LARGE \Red{ 19 - 24 September 1999,
%St John's College, Durham }}\\[1cm]
\Green{Athanasios Dedes}\\
\end{center}
\vskip 0.2 cm
\begin{center}
{\large   \sl   University of Bonn, Germany  } \\
\end{center}

\vskip 0.2 cm

\begin{center}
SUSY02, June 17-23, 2002, DESY Hamburg, Germany
\end{center}
\vskip1.0cm

\begin{center}
\fcolorbox{blau}{groguenc}{\textcolor{blau}{\fontsize{10mm}{16}
\begin{tabular}{c}
\sf       \phantom{  ..... ............... .....}     \\
\sf        \Red{{\bf $B_s \to \mu^+\mu^-$ and  Trilepton  Events     }} \\[0.7cm]
\sf \Red{{ \bf at the Tevatron
   }}\\
%\sf     \Red{{\bf  muon anomalous magnetic moment?  }} \\
% \\ \sf \Red{{\bf at hadron colliders in the MSSM}}    \\
\sf       \phantom{  ..... ............... .....}     \\
\end{tabular}}}
\end{center}

\vskip0.5cm
\begin{center}
\Green{In collaboration with:}\\[2mm]
\Red{H.~ Dreiner and U.~Nierste, 
Phys.\ Rev.\ Lett.\  {\bf 87}, 251804 (2001), {\tt hep-ph/0108037}} \\
\Blue{and}\\
\Red{H.~ Dreiner, U.~Nierste, and  P. Richardson, to appear} \\
\end{center}


\vskip1.5cm

%\LARGE{ \Blue{We show :}}
\Large{
\begin{enumerate}
\item \Blue{ The decay \bs ~in the  MSSM}
%\item \Blue{ \bs ~in mSUGRA and its correlation with the  $(g-2)_\mu$ }
\item \Blue{ \bs ~and its correlation with the Trilepton events at  Run II,
 $(g-2)_\mu$ and  Light Higgs Boson mass in the mSUGRA scenario. }
%\item \Blue{ Minimal SO(10) and \bs\ }
%\item \Blue{ Work to be done...}
\item \Blue{Conclusions}
\end{enumerate}
}


\vspace*{2cm}

See also SUSY02 talks by

 J. Urban, R. Arnowitt, C. Kolda, C. Balazs,  S. Baek, W. de Boer.

%%%%%%%%%%%%%%%%%%%%% LOGO %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{center}
% --
%\vspace*{0.5cm}
% \begin{tabular}{cc}
%   \mbox{\epsfxsize=2.2cm\epsfysize=1.8cm\epsffile{../ral/clrc.ps}} &
%   \mbox{\epsfxsize=2.0cm\epsfysize=2.0cm
%\epsffile{../ral/ppd.ps}}  \\
% \end{tabular}
% --
%\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{titlepage}


%
% ----------------------------------------
%
% ----------------------------------------
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Theory , Channels ...
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\include{susy}
%\include{mssm}
%\include{superpotential}
%\include{intro_msugra}
%\include{unification}
%\include{strong_CP}
%\include{edms_rparity}
%\include{bonn_conclusions}
%
\newpage
%
\CTran{The Experimental Facts}

\spa


\Green{$\surd$} \Blue{LEP Higgs boson mass bound (preliminary)}

%%%%%%%%%%%%%%%%%%%%%%
\begin{eqnarray}
M_h \ge 107 (113)~~{\rm GeV}~~~ \sin^2(\beta-\alpha)\simeq 1 
\label{higgsbound}
\end{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%


\Green{$\surd$} \Blue{The muon anomalous magnetic moment}

%%%%%%%%%%%%%%%%%%%   
\begin{equation}
-4.2 \times 10^{-10} \le \delta a_\mu^{\rm SUSY} \le 41.3 \times 10^{-10}
\;\;\;\; @90\% ~~{\rm CL}\nonumber
\label{g-2bound}  
\end{equation}
%%%%%%%%%%%%%%%%%%

\Green{$\surd$} \Blue{The CDF upper bound on $B_s$-meson decay to dimuons}


%%%%%%%%%%%%%%%%%%%   
\begin{equation}
\cbs < 2.0\times 10^{-6}
\;\;\;\; @90\% ~~{\rm CL}\nonumber 
\end{equation}
%%%%%%%%%%%%%%%%%%



\Green{$\surd$} \Blue{${\cal B}(b\to s\gamma)$}

[!conservative bound!]

%%%%%%%%%%%%%%%%%%%   
\begin{equation}
2.0\times 10^{-4} \le {\cal B}(b\to s\gamma)\le 5.0\times 10^{-4}
%\;\;\;\; @90\% ~~{\rm CL}
\nonumber 
\end{equation}
%%%%%%%%%%%%%%%%%%


\Green{$\surd$} \Blue{SUSY searches}

%%%%%%%%%%%%%%%%%%%   
\begin{equation}
......\;,m_{\tilde{\chi}^\pm_1} \gsim 100 ~~{\rm GeV},\;........
%\;\;\;\; @90\% ~~{\rm CL}
\nonumber 
\end{equation}
%%%%%%%%%%%%%%%%%%

%\newpage

%\CTran{Theory Status}

%\Green{$\surd$} \Blue{MSSM : \bs}




\newpage

\CTran{\bs~ vs. $\dam$ in the MSSM}

\spa

\Green{$\bullet$} \Blue{$\dam$ depends upon 7 parameters}
{\large (T. Moroi) }

%%%%%%%%%%%%%%%%%%%%%%55
\begin{eqnarray}
\dam &=& f(M_1\;,\; \Red{M_2} \;,\; A_\mu
\;,\; \Red{\mu} \;,\; \Red{\tan\beta} \;,\; m_{\tilde{\mu}_L}\;,\;
m_{\tilde{\mu}_R})\nonumber 
%\\[1cm]
%\cbs &=& f(M_2 \;,\; A_t \;,\; \mu \;,\; M_A \;,\;
%\tan\beta \;,\; M_{\tilde{t}_L}\;,\; M_{\tilde{t}_R}) \nonumber
\end{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%

\Green{$\bullet$} \Blue{$\cbs$ depends (mainly) upon 7 parameters}

%%%%%%%%%%%%%%%%%%%%%%55
\begin{eqnarray}
%\dam &=& f(M_1\;,\; \Red{M_2} 
%\;,\; \mu \;,\; \Red{\tan\beta} \;,\; m_{\tilde{\mu}_L}\;,\;
%m_{\tilde{\mu}_R})\nonumber 
%\\[1cm]
\cbs &=& f(M_2 \;,\; \Red{A_t} \;,\; \Red{\mu} \;,\;\Red{\tan\beta}  \;,\;
 \Red{M_A}\;,\; m_{\tilde{t}_L}\;,\; m_{\tilde{t}_R}) \nonumber
\end{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%

\Green{$\bullet$} \Blue{Approximately :}

%\Blue{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{eqnarray}
\cbs \simeq 3 \times 10^{-7} \biggl [\frac{m_\mu M_{B_s}}{M_W^2}\biggr ]^2
~ \frac{\tan^6\beta}{M_A^4} \mu^2  A_t^2 ~ C(m_{\tilde{t}},m_{\tilde{\chi}})
 \;,
\label{bmmapr}\nonumber
\end{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%}
{\large{\Red{MSSM}} :
{\large K.~S.~Babu and C.~Kolda, '99,\\
 \hspace*{1.9cm}C.~Huang,  W.~Liao and Q.~Yan, '99\\
\hspace*{1.9cm}P.~H.~Chankowski and L.~Slawianowska, '01,\\
 \hspace*{1.9cm}C.~Bobeth, T.~Ewerth, F.~Kruger and J.~Urban, '01, '02 \\
\hspace*{1.9cm}G. Isidori, A. Retico, '01,\\
\hspace*{1.9cm}C.~Bobeth, A.~J.~Buras, F.~Kruger and J.~Urban, Dec. '01,\\}
\large{\Red{mSUGRA}} :
A.~Dedes, H.~K.~Dreiner and U.~Nierste, '01 \\
\hspace*{2.0cm}R.~Arnowitt, B.~Dutta, T.~Kamon and M.~Tanaka, '02 \\
\hspace*{2.0cm}H.~Baer, C.~Balazs, A.~Belyaev, J.~K.~Mizukoshi, X.~Tata and Y.~Wang,'02\\
\large{\Red{GMSB, AMSB}} :
S.~w.~Baek, P.~Ko and W.~Y.~Song, '02
}





\newpage 

%\CTran{\bs ~vs. $(g-2)_\mu$ in the MSSM}

%\spa

%\spa

\centerline{\epsfig{figure=combinedbmmg-2.ps,height=7.5in,angle=90}}

\Green{$\bullet$} \Blue{The Maximum mass for the Lightest 
Observable SUSY particle (LOSP) } {\large [Feng and Matchev '01]}


%%%%%%%%%%%%%%5
\begin{eqnarray}
\dam &\simeq& 18\times 10^{-10} ~ \frac{\tan\beta}{50}
~ \biggl (\frac{603~{\rm GeV}}{M_{\rm LOSP}^{\rm max}} \biggr)^2 \;,\;
\nonumber 
\end{eqnarray}
%%%%%%%%%%%%%%%%%%%


\Green{$\bullet$} \Blue{The Maximum mass for the Heaviest Higgs Boson }


%%%%%%%%%%%%%%%
\begin{eqnarray}
\cbs &\simeq& 5\times 10^{-7}~\biggl (\frac{\tan\beta}{50}\biggr )^6
~\biggl (\frac{550~{\rm GeV}}{M_A^{\rm max}} \biggr )^4
%\nonumber \\ &+& 
%+8\times 10^{-9} \;. \label{bmmnum} 
\nonumber
\end{eqnarray}
%%%%%%%%%%%%%%%%


\newpage

\CTran{\bs ~vs. $(g-2)_\mu$ in mSUGRA }

\spa

{\large A.~Dedes, H.~K.~Dreiner and U.~Nierste, '01}

\spa

\centerline{\epsfig{figure=btomumu_m12tanb.ps,angle=90}}



Solid : $\cbs$

\Green{Dashed }: $\dam$ in $10^{-10}$ units

\Red{ Dot-dashed} : Higgs mass

 \Red{Shaded} : Excluded







\newpage

{\large A.~Dedes, H.~K.~Dreiner and U.~Nierste, '01}

\spa

\centerline{\epsfig{figure=btomumu_m12mo.ps,angle=90}}

\spa



Solid : $\cbs$

\Green{Dashed }: $\dam$ in $10^{-10}$ units

\Red{ Dot-dashed} : Higgs mass

 \Red{Shaded} : Excluded


\newpage
\CTran{Trileptons and \bs~  at Run II} 

\spa

\Green{$\bullet$} \Blue{The ``Gold-plated'' Mode}

\spa \spa \spa

%$\rightarrow$ 
%\Red{Trilepton final states, $lll$, $l^\pm l^\pm$}
%
%\Green{$\bullet$} \Blue{ $q \bar{q}' \stackrel{W}\rightarrow 
%\chi^\pm \chi_2^0%}
%
%\Red{$\bullet$} \Blue{ $\chi_1^\pm \rightarrow
%  (\tilde{l},\tilde{\tau}) \nu
%\rightarrow (l,\tau) \chi_1^0 \nu$
%
%\Red{$\bullet$} \Blue{ $\chi_1^\pm \rightarrow
%  (\tilde{l},\tilde{\tau}) \tilde{\nu}
%\rightarrow (l,\tau) \chi_1^0 \nu$
%\spa

\centerline{\epsfig{figure=tril.eps,height=5in}}



\newpage





\centerline{\epsfig{figure=chardecays.ps,height=7.0in}}


\Green{$\bullet$} \Blue{Final State :} \Red{ $lll$, $l^\pm l^\pm$, 
$l^\pm l^\mp \tau$,
$l^\pm \tau\tau$, $\tau\tau\tau$, $\tau^\pm\tau^\pm$}

$l\equiv e,\mu$ , focus on  $3{\rm L}\equiv lll$


\Green{$\surd$} \Blue{New and improved analysis compared to the one by
{\Black{\Large Matchev and Pierce '99 }} \Red{$\rightarrow$} slightly bigger 
signal over the Background}

\newpage

%\CTran{Trileptons}

 

{\large A. Dedes, H. Dreiner, U. Nierste, P. Richardson '02}

\spa

\centerline{\epsfig{figure=tan5lll.ps,angle=90}}

\Green{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=2fb^{-1}$}

\Blue{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=10fb^{-1}$}

\Magenta{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=30fb^{-1}$}

Dashed : $\dam$ in $10^{-10}$ units

Dotted : Light Higgs Boson mass 


\newpage



%{\large A. Dedes, H. Dreiner, U. Nierste, P. Richardson '02}
\spa


\centerline{\epsfig{figure=tan50lll.ps,angle=90}}


\Green{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=2fb^{-1}$}

\Blue{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=10fb^{-1}$}

\Magenta{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=30fb^{-1}$}

Solid : $\cbs$

Dashed : $\dam$ in $10^{-10}$ units

Dotted : Light Higgs Boson mass 


\newpage

%\CTran{3L Nightmare scenario}
%
%{\small A. Dedes, H. Dreiner, U. Nierste, P. Richardson}
%
%\spa\spa
%
%\centerline{\epsfig{figure=m300lll.ps,angle=90}}
%
%
%\CTran{3L Most Optimistic scenario}

%{\small A. Dedes, H. Dreiner, U. Nierste, P. Richardson}

\spa

\centerline{\epsfig{figure=m150lll.ps,angle=90}}


\Green{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=2fb^{-1}$}

\Blue{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=10fb^{-1}$}

\Magenta{Tevatron 5$\sigma$ reach for 3L and ${\cal L}=30fb^{-1}$}

Solid : $\cbs$

Dashed : $\dam$ in $10^{-10}$ units

Dotted : Light Higgs Boson mass 

\CTran{Conclusions}

\spa\spa

\Green{$\surd$} \Blue{ If \bs~ is observed at the Tevatron with 
${\cal L}=2 fb^{-1}$ [$\cbs \gsim 5\times 10^{-7}$]
 then :}

\underline{\Red{MSSM}}

\begin{itemize}

\item the heaviest Higgs boson mass is bounded from
above in the  MSSM, $M_A \lsim 550$ GeV

\item upper bound on  the ratio $A_t/M_A$ 

\item
strong support for the minimal SUSY SO(10) model

\end{itemize}



\underline{\Red{mSUGRA}}

\Green{$\surd$} \Blue{ If \bs~ is observed at the Tevatron Run II
 [$\cbs \gsim  10^{-8}$] then :}

\begin{itemize}

\item  $\dam$  deviates significantly from zero

\item $m_h^{max} \lsim 120$ GeV 

\item  \bs ~complements the trilepton searches

\item a  No-Lose scenario for mSUGRA  at the Tevatron 
with $M_{1/2} \;,\; M_0 \lsim 400$ and $\tan\beta  \gsim 40$

\end{itemize}

\spa






\spa \spa

%\Green{$\surd$} \Blue{At any  GUT model working at  large $\tan\beta\gsim 40$,
%the decay \bs ~should be  consider as a constraint or as a prediction.}

{\tt It might be that these are the SUSY footprints at Tevatron.......}

\end{document}





