\@doendnote {41}{We do not consider new CP-violating phases which could occur in $\mu $ and $A_0$.}
\@doendnote {42}{ In the mSUGRA analysis below, $m_t(m_t)$ is not fixed due the variation of the strong coupling $\alpha _s$ with the SUSY spectrum under the assumption of the unification of the gauge couplings. However, the effect of this variation is small compared to the hadronic uncertainty.}
\@doendnote {43}{We neglect the operators $O_S^\prime = m_s(\mathaccent "7016\relax {s}_\alpha P_L b_\alpha )(\mathaccent "7016\relax {\mu }\mu )$ and $O_P^\prime = m_s(\mathaccent "7016\relax {s}_\alpha P_L b_\alpha )(\mathaccent "7016\relax {\mu }\gamma _5\mu )$ since they are 50 times smaller then the leading $m_b$ ones. For large values of $\mathop {\mathgroup \symoperators tan}\nolimits \beta $ the $m_s\mathop {\mathgroup \symoperators tan}\nolimits ^3\beta $ Wilson coefficients, $c_{S,P}^\prime $ could be only comparable with the $m_b\mathop {\mathgroup \symoperators tan}\nolimits ^2\beta $ coefficients $c_{S,P}$ but not competitive to the leading $m_b\mathop {\mathgroup \symoperators tan}\nolimits ^3\beta $ self energy $c_{P,S}$'s.}
\@doendnote {44}{In the case of the Higgs mass the word ``large" means $\mathop {\mathgroup \symoperators tan}\nolimits \beta \lower .7ex\hbox {$\mskip \thickmuskip \mathrel {\mathop {\sim }\limits ^{\textstyle >}}\mskip \thickmuskip $}10$, in the case of the muon $g-2$, $\mathop {\mathgroup \symoperators tan}\nolimits \beta \lower .7ex\hbox {$\mskip \thickmuskip \mathrel {\mathop {\sim }\limits ^{\textstyle >}}\mskip \thickmuskip $}20$ and as we will see in the case of $B_s\rightarrow \mu ^+\mu ^-$, $\mathop {\mathgroup \symoperators tan}\nolimits \beta \lower .7ex\hbox {$\mskip \thickmuskip \mathrel {\mathop {\sim }\limits ^{\textstyle >}}\mskip \thickmuskip $}40$.}
\@doendnote {45}{The value for the trilinear soft SUSY breaking couplings, $A_0$ is set to zero throughout this analyses. We have explicitly check that its variation within $\pm $500 GeV modifies our result for $B_s\rightarrow \mu ^+\mu ^-$within the $f_{B_s}$ error. We leave it out here in order to make the analysis simpler.}
\@doendnote {46}{The upper limit comes from the REWSB requirement.}
\@doendnote {47}{Actually this point coincides with the point L quoted in \cite {Ellis}.}
\@doendnote {48}{Needed not to comply with $g-2$ and $b\rightarrow s\gamma $ constraints.}