More model-independent analysis of b→s processes

We study model-independently the implications of nonstandard scalar and pseudoscalar interactions for the decays $\stackrel{\ensuremath{\rightarrow}}{b}s\ensuremath{\gamma},$ $\stackrel{\ensuremath{\rightarrow}}{b}sg,$ $\stackrel{\ensuremath{\rightarrow}}{b}s{\mathcal{l}}^{+}{\mathcal{l}}^{\ensuremath{-}}$ $(\mathcal{l}=e,\ensuremath{\mu})$ and ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}.$ We find sizable renormalization effects from scalar and pseudoscalar four-quark operators in the radiative decays and at $O({\ensuremath{\alpha}}_{s})$ in hadronic b decays. Constraints on the Wilson coefficients of an extended operator basis are worked out. Further, the ratios ${R}_{H}=\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{B}H{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})/\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{B}{\mathrm{He}}^{+}{e}^{\ensuremath{-}}),$ for ${H=K}^{(*)}{,X}_{s},$ and their correlations with the ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ 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, ${R}_{H}{=1+O(m}_{\ensuremath{\mu}}^{2}{/m}_{b}^{2}),$ has a much smaller theoretical uncertainty $(\ensuremath{\lesssim}1%)$ than the one for the individual branching fractions. The present experimental limit ${R}_{K}l~1.2$ puts constraints on scalar and pseudoscalar couplings, which are similar to the ones from current data on $\mathcal{B}{(B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}).$ We find that new physics corrections to ${R}_{{K}^{*}}$ and ${R}_{{X}_{s}}$ can reach 13% and 10%, respectively.