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\author{\sf Athanasios Dedes}
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\begin{document}
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\date{30/6/2000}
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\Trtitle{\sf  Correlation of $B_s \to \mu^+\mu^-$ and $(g-2)_\mu$ in Minimal
  Supergravity, ~~~~~~~~~~~ {\tt hep-ph/0108037}}
%
\Large
\sf
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\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}

\vskip1.0cm

\begin{center}
\fcolorbox{blau}{groguenc}{\textcolor{blau}{\fontsize{10mm}{16}
\begin{tabular}{c}
\sf       \phantom{  ..... ............... .....}     \\
\sf        \Red{{\bf Correlation of $B_s \to \mu^+\mu^-$ and $(g-2)_\mu$ }} \\
\sf \Red{{ \bf  in Minimal
  Supergravity   }}\\
%\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, {\tt hep-ph/0108037}} \\
\end{center}


\vskip0.5cm

\LARGE{ \Blue{We show :}}
\Large{
\begin{enumerate}
\item \Blue{ the decay \bs\ is a stringent test of the mSUGRA scenario
    with large $\tan\beta \gsim 35$, in
particular when correlated with $(g-2)_\mu$ }\\
\item \Blue{ if $(g-2)_\mu$ exceeds the Standard Model
  prediction by $30\cdot 10^{-10}$, 
  $\cbs$ is larger by a factor of 100
  than in the Standard Model and well within reach of Run-II of the
  Tevatron. }\\
\item \Blue{Higgs masses less than 119 GeV are correlated
with an enhancement of $\cbs$ over the SM value by two orders of
magnitude.  }\\
\item \Blue{$\cbs$ and $(g-2)_\mu$ : a threat or discovery for SO(10) GUTS!  }
\end{enumerate}
}


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\end{titlepage}


%
% ----------------------------------------
%
% ----------------------------------------
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Theory , Channels ...
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\include{phases}
%\include{strong_CP}
%\include{edms_rparity}
%\include{bonn_conclusions}
%
\newpage
%%%%%%%%%%%%%%%% PAGE 1 %%%%%%%%%%%%%%%%%

\Green{$\bullet$} \Blue{Based on Davier-H\"ocker calculation for the
  Hadronic
contributions to the muon 
$g-2$, BNL reports a 2.6$\sigma$ deviation from the SM}

\spa


There are four possible interpretations
of this discrepancy :
\begin{itemize}

\item a statistical fluctuation with 0.9\% probability.


\item something is ``wrong'' with the experiment


\item something is ``wrong'' with the theoretical analysis of the
hadronic  and/or the light by light contribution to
the muon anomalous magnetic moment.



\item the by far most exciting possibility: 
\end{itemize}


%\Green{$\bullet$} 
\Blue{
    there is \Red{``New Physics''}~ BSM}
\begin{eqnarray}
21.5 \times 10^{-10} \lsim \delta a_\mu^{NP} \lsim 63.7\times 10^{-10}
\;\;\;\;
{\rm @ 90 \% ~CL}\nonumber
\end{eqnarray}
\begin{itemize}

\item{\Blue{$\delta a_\mu^{NP}$ is positive}}

\item{\Blue{$\delta a_\mu^{NP}$ is of the same order of the EW
      contributions, 
$\delta a_\mu^{NP} \propto \frac{G_F m_\mu^2}{4\pi^2\sqrt{2}}$}}
\spa

\end{itemize}
\bc
\Green{$\bullet$} \Blue{mSUGRA}
\ec

\spa

\bc
\huge\Red{$(\delta a_\mu)_{SUSY}\propto~\tan\beta~\frac{
f(M_0)}{M_{1/2} ^2}$}
\ec

\spa 

\Blue{~~~~~~~~invites large $\tan\beta \gsim 10$ and $M_{1/2}\lsim
  750$ GeV}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage


\Green{$\bullet$} \Blue{SUSY modifies B-meson observables if
  $\tan\beta$
is large [$\Rightarrow Y_b$ large ]}

\Green{$\bullet$} \Blue{Especially sencitive observables : $ B\rightarrow
  X_s \gamma , B\rightarrow l^+ l^- $}


\begin{itemize}

\item $B\rightarrow X_s \gamma$ : relies on a cancelation between
$H^\pm-t$ and $\tilde{\chi}-\tilde{t}$ loops.

\item $B\rightarrow l^+ l^- $ : large for large $\tan\beta$, almost 
independent from the sign of $\mu$ 

\end{itemize}


\spa

\centerline{\epsfig{figure=self.eps}}

\spa



\bc
\Red{\huge $\cbs \propto \frac{\tan^6\beta}{M_{1/2}^2}$}
\ec

\spa

So, 

\bc
\Red{\huge$\cbs \propto \frac{\tan^5\beta ~~(\delta a_\mu)_{SUSY}}{f(M_0)}$}
\ec






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage
\Green{$\bullet$} \Blue{Standard Model :}

\spa 
\bc
\begin{eqnarray}
\cbs  =(3.7 \pm 1.2) \times 10^{-9}~~~~{\rm very~~ small!}
\nonumber
\end{eqnarray}
\ec

\spa 

\Green{$\bullet$} \Blue{Only an experimental bound from CDF Run~I}

\spa

\bc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{eqnarray}
\cbs < 2.6 \times 10^{-6},
\qquad \mbox{ at 95\% C.L.} 
\nonumber
\end{eqnarray}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ec

\spa 

\Green{$\bullet$} \Blue{Future experiment: CDF Run IIa and IIb}

\Red{$\rightarrow$} \Blue{ $5 \times 10^{-7}$ for 50  events  with luminosity
  2 $fb^{-1}$}

\Red{$\rightarrow$} \Blue{ $5 \times 10^{-7}$ for 250-500 events  
with luminosity
  10-20 $fb^{-1}$}

\spa 


\begin{eqnarray}
\lefteqn{\!\! \cbs \; =} \nn 
&& 6.0 \cdot 10^{-7} 
\lt(\frac{|V_{ts}|}{0.040}\rt)^2
\lt(\frac{f_{B_s}}{230\,\mev}\rt)^2
\frac{m_{\mu}^2}{m_{B_s}^2}
\sqrt{1-\frac{4 m_\mu^2}{m_{B_s}^2}} \nonumber \\[0.5cm]
 && \Biggl \{
 \biggl ( 1-\frac{4 m_\mu^2}{M_{B_s}^2}\biggr ) 
  \lt| \frac{m_{B_s}^2 C_S}{m_{\mu}} \rt|^2 + 
 \lt| \frac{m_{B_s}^2 C_P}{m_{\mu}} - 2 C_A \rt|^2 \Biggr \} .
 \nonumber
\end{eqnarray}

\spa


\bc
\Blue{
$C^{self-SUSY}_P, C^{self-SUSY}_S \propto \tan^3\beta$ \\[1cm]
$C_A$ is tha SM contribution from $t-W$ penguins $t-W-\nu$ box. 
}
\ec

\newpage

\vspace*{1cm}

\Blue{mSUGRA point: $M_{1/2}=450, M_0=350, A_0=0, \mu>0, m_t=175$ GeV}

\vspace*{2cm}

\centerline{\epsfig{figure=btomumu-g-2.ps,angle=90}}

\newpage

\vspace*{3cm}

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




\newpage

\vspace*{3cm}

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


\newpage

\spa

\Green{$\bullet$} \Blue{Large $\tan\beta$ is well motivated in SO(10)}

\vspace*{2cm}

\Green{$\bullet$} \Blue{In order to avoid various constraints [mainly
  proton decay, $b\rightarrow s\gamma$, $g-2$ and REWSB] it
  requires : breaking of universality for the Higgs masses, and 
  $M_{1/2}<<M_0$.}


\vspace*{2cm}

 Example [after a fit] : $M_A=110$ GeV, $\tan\beta\simeq
50$,
$A_t \gsim, 1$ TeV, $m_{\tilde{t}}<1$ TeV, $m_{\tilde{\chi}}<250$ GeV
implies :


\vspace*{2cm}

\bc
\Red{$\cbs \gsim 10^{-5}~~~~{\rm already~~ excluded~~ by~~ CDF}$}
\ec

\vspace*{2cm}


\Blue{A way out \Red{$\rightarrow$} relax Yukawa unification up to  5-10\%
and you are just around the corner of the \bs~~ to be discovered at CDF
Run~IIa !!} 



\newpage

\spa

\CTran{Conclusions}

\spa

\Green{$\surd$} \Blue{Striking correlation between the muon
anomalous magnetic moment $a_{\mu}$ and the branching ratio $\cbs$ in
mSUGRA scenarios.}

\spa

\Green{$\surd$} \Blue{If the reported excess in $a_{\mu}$  is
caused by mSUGRA corrections with large $\tan\beta$, one faces more
than an order of magnitude enhancement of $\cbs$ over its SM value.}

\spa

\Green{$\surd$} \Blue{Well within reach of Run-II of the Tevatron.}


\spa

\Green{$\surd$} \Blue{The two combined measurements 
significantly constrain the mSUGRA parameters,
allowing a
determination of $\tan\beta$ and $M_{1/2}$. }

\spa

\Green{$\surd$} \Blue{A measurement of $\cbs$
will further constrain the mass of the lightest Higgs boson.}

\spa

\Green{$\surd$} \Blue{SO(10)
SUSY explanations of the measured $a_{\mu}$ are barely compatible with
the present upper bound on $\cbs$.}







\end{document}





