\relax \bibstyle{apsrev} \citation{mSUGRA} \citation{history} \citation{BNL} \citation{Feng} \citation{Nath} \citation{Nanopoulos} \citation{Arnowitt} \citation{Choi} \citation{Martin} \citation{Gomez} \citation{Kim} \citation{Sven} \citation{Barger} \citation{Fauzi} \citation{Roszkowski} \citation{Lahanas} \citation{Masiero} \citation{Masiero} \citation{Urban} \citation{Babu} \citation{Chankowski} \citation{Urban} \citation{Babu} \citation{Chankowski} \citation{cgnw} \newlabel{FirstPage}{{}{1}} \citation{cgnw} \citation{BNL} \citation{LEPhiggs} \citation{mSUGRA} \citation{Feng} \citation{Lahanas} \citation{ASBS} \citation{Burasreview} \citation{fbs} \citation{CDFbmumu} \citation{LHCb} \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} \newlabel{heff}{{1}{2}} \newlabel{smbmumu}{{2}{2}} \newlabel{expbmumu}{{3}{2}} \citation{Urban} \citation{REWSB} \citation{ASBS} \citation{CDFbmumu} \citation{BNL} \citation{Nierste} \citation{LEPhiggs} \newlabel{hamiltonian}{{4}{3}} \newlabel{operators}{{7}{3}} \newlabel{brancing}{{8}{3}} \citation{Roszkowski} \citation{Shadmi} \citation{Stuart} \citation{Baer} \citation{Stuart} \citation{CDFbmumu} \bibcite{BNL}{{1}{}{{}}{{}}} \bibcite{LEPhiggs}{{2}{}{{}}{{}}} \bibcite{mSUGRA}{{3}{}{{}}{{}}} \bibcite{history}{{4}{}{{}}{{}}} \citation{mSUGRA} \bibcite{Feng}{{5}{}{{}}{{}}} \bibcite{Nath}{{6}{}{{}}{{}}} \bibcite{Nanopoulos}{{7}{}{{}}{{}}} \bibcite{Arnowitt}{{8}{}{{}}{{}}} \bibcite{Choi}{{9}{}{{}}{{}}} \bibcite{Martin}{{10}{}{{}}{{}}} \bibcite{Gomez}{{11}{}{{}}{{}}} \bibcite{Kim}{{12}{}{{}}{{}}} \bibcite{Sven}{{13}{}{{}}{{}}} \bibcite{Barger}{{14}{}{{}}{{}}} \bibcite{Fauzi}{{15}{}{{}}{{}}} \bibcite{Roszkowski}{{16}{}{{}}{{}}} \bibcite{Lahanas}{{17}{}{{}}{{}}} \bibcite{cgnw}{{18}{}{{}}{{}}} \bibcite{ASBS}{{19}{}{{}}{{}}} \bibcite{Burasreview}{{20}{}{{}}{{}}} \bibcite{fbs}{{21}{}{{}}{{}}} \bibcite{CDFbmumu}{{22}{}{{}}{{}}} \bibcite{LHCb}{{23}{}{{}}{{}}} \bibcite{Inami}{{24}{}{{}}{{}}} \bibcite{Krawczyk}{{25}{}{{}}{{}}} \bibcite{Buchalla}{{26}{}{{}}{{}}} \bibcite{He}{{27}{}{{}}{{}}} \bibcite{Nierste}{{28}{}{{}}{{}}} \bibcite{Urban}{{29}{}{{}}{{}}} \bibcite{Choudhury}{{30}{}{{}}{{}}} \bibcite{Babu}{{31}{}{{}}{{}}} \bibcite{Chankowski}{{32}{}{{}}{{}}} \bibcite{Maxim}{{33}{}{{}}{{}}} \bibcite{Masiero}{{34}{}{{}}{{}}} \bibcite{Ali}{{35}{}{{}}{{}}} \bibcite{REWSB}{{36}{}{{}}{{}}} \bibcite{Ellis}{{37}{}{{}}{{}}} \bibcite{Shadmi}{{38}{}{{}}{{}}} \bibcite{Stuart}{{39}{}{{}}{{}}} \bibcite{Baer}{{40}{}{{}}{{}}} \global \chardef \firstnote@num40\relax \bibcite{endnote41}{{41}{}{{}}{{}}} \bibcite{endnote42}{{42}{}{{}}{{}}} \bibcite{endnote43}{{43}{}{{}}{{}}} \bibcite{endnote44}{{44}{}{{}}{{}}} \bibcite{endnote45}{{45}{}{{}}{{}}} \bibcite{endnote46}{{46}{}{{}}{{}}} \bibcite{endnote47}{{47}{}{{}}{{}}} \citation{Ellis} \bibcite{endnote48}{{48}{}{{}}{{}}} \newlabel{LastBibItem}{{48}{5}} \citation{CDFbmumu} \citation{CDFbmumu} \citation{BNL} \citation{BNL} \newlabel{LastPage}{{}{5}} \global\NAT@numberstrue \@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 $B_s\rightarrow \mu ^+\mu ^-$\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 $B_s\rightarrow \mu ^+\mu ^-$\nobreakspace {} together with the SM prediction and the present bound by CDF\nobreakspace {}\cite {CDFbmumu}, $B_s\rightarrow \mu ^+\mu ^-$$ < 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.}}{6}} \newlabel{fig1}{{1}{6}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Contour plots (solid lines) of the predicted Branching Ratio $B_s\rightarrow \mu ^+\mu ^-$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. }}{6}} \newlabel{fig2}{{2}{6}}