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The rare decays B_s -> \mu^+\mu^- and B -> K^{(*)}\mu^+\mu^- are sensitive tonew particles and couplings via their interferences with the standard modelcontributions. Recently, the upper bound on B(B_s -> \mu^+\mu^-) has beenimproved significantly by the CMS, LHCb, CDF, and D{\O} experiments. Combiningwith the measurements of B(B-> K^{(*)}\mu^+\mu^-), we derive constraints on therelevant parameters of minimal supersymmetic standard model with and withoutR-parity, and examine their contributions to the dimuon forward-backwardasymmetry in B-> K^{*}\mu^+\mu^- decay. We find that (i) the contribution ofR-parity violating coupling products\lambda^{\prime}_{2i2}\lambda^{\prime*}_{2i3} due to squark exchange iscomparable with the theoretical uncertainties in B-> K \mu^+\mu^- decay, butstill could be significant in B-> K^{*}\mu^+\mu^- decay and could account forthe forward-backward asymmetry in all dimuon invariant mass regions; (ii) theconstrained mass insertion (\delta^{u}_{LL})_{23} could have significantcontribution to dA_{FB}(B-> K^{*}\mu^+\mu^-)/ds, and such effects are favoredby thr recent results of the Belle, CDF, and LHCb experiments.

Revisiting B_s\to\mu^+\mu^- and B\to K^{(*)}\mu^+\mu^- decays in the MSSM with and without R-parity