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.
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