Probing extended Higgs sector through rare b --> s mu+ mu- transitions

We study the constraints on the contribution of new physics in the form of scalar/pseudoscalar operators to the average forward backward asymmetry <A_{FB}> of muons in B --> K mu+ mu- and the longitudinal polarization asymmetry A_{LP} of muons in B_s --> mu+ mu-. We find that the maximum possible value of <A_{FB}> allowed by the present upper bound on B(B_s --> mu+ mu-) is about 1% at 95% C.L. and hence will be very difficult to measure. On the other hand, the present bound on B(B_s --> mu+ mu-) fails to put any constraints on A_{LP}, which can be as high as 100% even if B(B_s --> mu+ mu-) is close to its standard model prediction. The measurement of A_{LP} will be a direct evidence for an extended Higgs sector, and combined with the branching ratio B(B_s --> mu+ mu-) it can even separate the new physics scalar and pseudoscalar contributions.