Probing the extended Higgs sector through rare b&#8594;s&#956;<SUP>+</SUP>&#956;<SUP>−</SUP> transitions

We study the constraints on the contribution of new physics in the form of scalar/pseudoscalar operators to the average forward-backward asymmetry &#8249;AFB&#8250; of muons in B&#8594;K&#956;+&#956;− and the longitudinal polarization asymmetry ALP of muons in Bs&#8594;&#956;+&#956;−. We find that the maximum possible value of &#8249;AFB&#8250; allowed by the present upper bound on B(Bs&#8594;&#956;+&#956;−) is about 1% at 95% C.L. and hence will be very difficult to measure. On the other hand, the present bound on B(Bs&#8594;&#956;+&#956;−) fails to put any constraints on ALP, which can be as high as 100% even if B(Bs&#8594;&#956;+&#956;−) is close to its standard model prediction. The measurement of ALP will be a direct evidence for an extended Higgs sector, and combined with the branching ratio B(Bs&#8594;&#956;+&#956;−) it can even separate the new physics scalar and pseudoscalar contributions