We study model-independently the implications of nonstandard scalar and pseudoscalar interactions for the decays $\overrightarrow{b}s\gamma ,$ $\overrightarrow{b}sg,$ $\overrightarrow{b}s{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ $(\mathcal{l}=e,\mu )$ and $B_s\to {\mu }^{+}{\mu }^{-}.$ We find sizable renormalization effects from scalar and pseudoscalar four-quark operators in the radiative decays and at $O\left({\alpha }_s\right)$ in hadronic b decays. Constraints on the Wilson coefficients of an extended operator basis are worked out. Further, the ratios $R_H=\mathcal{B}\left(\overrightarrow{B}H{\mu }^{+}{\mu }^{-}\right)/\mathcal{B}\left(\overrightarrow{B}{\mathrm{He}}^{+}{e}^{-}\right),$ for ${H=K}^{\left(*\right)}{,X}_s,$ and their correlations with the $B_s\to {\mu }^{+}{\mu }^{-}$ 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, $R_H{=1+O(m}_{\mu }^2{/m}_b^2),$ has a much smaller theoretical uncertainty $(\lesssim 1\%)$ 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 $\mathcal{B}{(B}_s\to {\mu }^{+}{\mu }^{-}).\mathrm{}$ We find that new physics corrections to $R_{K^{*}}$ and $R_{X_s}$ can reach 13% and 10%, respectively.

• Received 28 October 2003

DOI:https://doi.org/10.1103/PhysRevD.69.074020