Analysis of $B_s\to \phi\mu^+\mu^-$ decay within supersymmetry

Motivated by the first measurement on $\mathcal{B}(B_s\to\phi \mu^+\mu^-)$ by the CDF Collaboration, we study the supersymmetric effects in semi-leptonic $B_s\to\phi\mu^+\mu^-$ decay. In our evaluations, we analyze the dependences of the dimuon invariant mass spectrum and the forward-backward asymmetry on relevant supersymmetric couplings in the MSSM with and without R-parity. The analyses show the new experimental upper limits of $\mathcal{B}(B_s\to\mu^+\mu^-)$ from the LHCb Collaboration could further improve the bounds on sneutrino exchange couplings and $(\delta^u_{LL})_{23}$ as well as $(\delta^d_{LL,RR})_{23}$ mass insertion couplings. In addition, within the allowed ranges of relevant couplings under the constraints from $\mathcal{B}(B_s\to\phi \mu^+\mu^-)$, $\mathcal{B}(B\to K^{(*)}\mu^+\mu^-)$ and $\mathcal{B}(B_s\to \mu^+\mu^-)$, the dimuon forward-backward asymmetry and the differential dimuon forward-backward asymmetry of $B_s\to\phi\mu^+\mu^-$ are highly sensitive to the squark exchange contribution and the $(\delta^u_{LL})_{23}$ mass insertion contribution. The results obtained in this work will be very useful in searching supersymmetric signal at the LHC.