Bayesian Fit of Exclusive $b\to s\bar{\ell }\ell$ Decays: The Standard Model Operator Basis

Abstract

We perform a model-independent fit of the short-distance couplings $C_{7,9,10}$ within the Standard Model set of $b\to s\gamma$ and $b\to s\bar{\ell }\ell$ operators. Our analysis of $B\to K^{\ast }\gamma$, $B\to K^{(\ast )}\bar{\ell }\ell$ and $B_s\to \bar{\mu }\mu$ decays is the first to harness the full power of the Bayesian approach: all major sources of theory uncertainty explicitly enter as nuisance parameters. Exploiting the latest measurements, the fit reveals a flipped-sign solution in addition to a Standard-Model-like solution for the couplings $C_i$. Each solution contains about half of the posterior probability, and both have nearly equal goodness of fit. The Standard Model prediction is close to the best-fit point. No New Physics contributions are necessary to describe the current data. Benefitting from the improved posterior knowledge of the nuisance parameters, we predict ranges for currently unmeasured, optimized observables in the angular distributions of $B\to K^{\ast }(\to K\pi )\bar{\ell }\ell$.

Comments: 42 pages, 8 figures; v2: Using new lattice input for f_Bs, considering Bs-mixing effects in BR[B_s->ll]. Main results and conclusion unchanged, matches journal version