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Analysis of $B_s\to ϕμ^+μ^-$ decay within supersymmetry

Motivated by the first measurement on $\mathcal{B}(B_s\toϕμ^+μ^-)$ by the CDF Collaboration, we study the supersymmetric effects in semi-leptonic $B_s\toϕμ^+μ^-$ 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 $\mathcal{B}(B_s\toμ^+μ^-)$ from the LHCb Collaboration could further improve the bounds on sneutrino exchange couplings and $(δ^u_{LL})_{23}$ as well as $(δ^d_{LL,RR})_{23}$ mass insertion couplings. In addition, within the allowed ranges of relevant couplings under the constraints from $\mathcal{B}(B_s\toϕμ^+μ^-)$, $\mathcal{B}(B\to K^{(*)}μ^+μ^-)$ and $\mathcal{B}(B_s\to μ^+μ^-)$, the dimuon forward-backward asymmetry and the differential dimuon forward-backward asymmetry of $B_s\toϕμ^+μ^-$ are highly sensitive to the squark exchange contribution and the $(δ^u_{LL})_{23}$ mass insertion contribution. The results obtained in this work will be very useful in searching supersymmetric signal at the LHC.