\relax \citation{BNL} \citation{LEPhiggs} \citation{mSUGRA} \citation{Feng} \citation{Lahanas} \citation{ASBS} \citation{Burasreview} \citation{fbs} \citation{CDFbmumu} \citation{LHCb} \newlabel{smbmumu}{{1}{1}} \newlabel{expbmumu}{{2}{1}} \citation{Inami} \citation{Krawczyk} \citation{Buchalla} \citation{He} \citation{Chankowski} \citation{Nierste} \citation{Urban} \citation{Maxim} \citation{Babu} \citation{Urban} \citation{Burasreview} \citation{Masiero} \citation{Ali} \citation{Urban} \newlabel{hamiltonian}{{3}{2}} \newlabel{operators}{{4}{2}} \citation{REWSB} \citation{ASBS} \citation{Ellis} \citation{CDFbmumu} \citation{BNL} \citation{Nierste} \newlabel{brancing}{{5}{3}} \citation{LEPhiggs} \citation{Roszkowski} \citation{Shadmi} \citation{Stuart} \citation{Baer} \citation{Stuart} \citation{CDFbmumu} \bibcite{BNL}{1} \bibcite{LEPhiggs}{2} \bibcite{mSUGRA}{3} \bibcite{Feng}{4} \bibcite{Nath}{5} \bibcite{Nanopoulos}{6} \bibcite{Arnowitt}{7} \bibcite{Choi}{8} \bibcite{Martin}{9} \bibcite{Gomez}{10} \bibcite{Kim}{11} \bibcite{Sven}{12} \bibcite{Barger}{13} \bibcite{Fauzi}{14} \bibcite{Roszkowski}{15} \bibcite{Lahanas}{16} \bibcite{ASBS}{17} \bibcite{Burasreview}{18} \bibcite{fbs}{19} \bibcite{CDFbmumu}{20} \bibcite{LHCb}{21} \bibcite{Inami}{22} \bibcite{Krawczyk}{23} \bibcite{Buchalla}{24} \bibcite{He}{25} \bibcite{Nierste}{26} \bibcite{Urban}{27} \bibcite{Choudhury}{28} \bibcite{Babu}{29} \bibcite{Chankowski}{30} \bibcite{Huang}{31} \bibcite{Maxim}{32} \bibcite{Masiero}{33} \bibcite{Ali}{34} \bibcite{REWSB}{35} \bibcite{Ellis}{36} \bibcite{Shadmi}{37} \bibcite{Stuart}{38} \bibcite{Baer}{39} \citation{CDFbmumu} \citation{CDFbmumu} \citation{BNL} \citation{BNL} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The predicted SUSY contribution to the muon anomalous magnetic $\delta a_\mu $ (bottom), versus the predicted branching ratio $\mathaccent "7016\relax {B}_s\rightarrow \mu ^+\mu ^-$\nobreakspace {}\nobreakspace {} (left) for the input values of $\mathop {\mathgroup \symoperators tan}\nolimits \beta $ (top) in an indicative mSUGRA point [$M_{1/2}=450, M_0=350, A_0=0, \mu >0, m_t=175$ GeV]. We plot the both LO and NLO corrections to $\mathaccent "7016\relax {B}_s\rightarrow \mu ^+\mu ^-$\nobreakspace {}\nobreakspace {} together with the SM prediction and the present bound by CDF\nobreakspace {}\cite {CDFbmumu}, $\mathaccent "7016\relax {B}_s\rightarrow \mu ^+\mu ^-$\nobreakspace {}$ < 2.6\times 10^{-6}$ at 95\% CL. The regions where the SUSY contribution to the muon anomalous magnetic moment is such that the present deviation with the SM is recovered at $1\sigma $ and $2\sigma $ is also shown. $f_{B_s}$ has been chosen to be 230 MeV.}}{9}} \newlabel{fig1}{{1}{9}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Contour plots (solid lines) of the predicted Branching Ratio $\mathaccent "7016\relax {B}_s\rightarrow \mu ^+\mu ^-$\nobreakspace {}on the plane $M_{0},M_{1/2}$ in the mSUGRA scenario and for $\mathop {\mathgroup \symoperators tan}\nolimits \beta =50, A_0=0, \mu >0, m_t=175$ GeV. The fully shaded region is excluded from both theoretical [REWSB(left-upper corner),not neutralino LSP(down)] and experimental [susy and higgs searches (mainly left strip till 1 TeV $M_0$ approximately)] facts. The shaded-dotted region shows the prediction of this mSUGRA point for the muon anomalous magnetic moment [in units $10^{-10}$] being within $2\sigma $ of the value reported in \cite {BNL}. Contours with the light Higgs boson mass equal to 115,120,121 are also shown (dotted-dashed lines). Here $f_{B_s}=230$ MeV. }}{10}} \newlabel{fig2}{{2}{10}}