  We study model-independently the implications of non-standard scalar and
pseudoscalar interactions for the decays b ->s gamma, b -> s g, b -> s l^+l^-
(l=e,mu) and B_s -> mu^+ mu^-. We find sizeable renormalization effects from
scalar and pseudoscalar four-quark operators in the radiative decays and at
O(alpha_s) in hadronic b decays. Constraints on the Wilson coefficients of an
extended operator basis are worked out. Further, the ratios R_H = BR(B -> H
mu^+ mu^-)/BR(B -> H e^+ e^-), for H=K^(*), X_s, and their correlations with
B_s -> mu^+ mu^- decay are investigated. We show that the Standard Model
prediction for these ratios defined with the same cut on the dilepton mass for
electron and muon modes, R_H= 1 + O(m^2_mu/m^2_b), has a much smaller
theoretical uncertainty (<1%) than the one for the individual branching
fractions. The present experimental limit R_K < 1.2 puts constraints on scalar
and pseudoscalar couplings, which are similar to the ones from current data on
BR(B_s -> mu^+ mu^-). We find that new physics corrections to R_{K*} and
R_{X_s} can reach 13% and 10%, respectively.
