Anatomy of a six-parameter fit to the $b\to s \ell^+\ell^-$ anomalies

Abstract

Discrepancies between measurements of decay modes with an underlying quark level transition $b\to s \ell^+\ell^-$ and standard model (SM) predictions have persisted for several years, particularly for the muon channels. The inadequacy of the SM becomes more compelling in a global fit. For example, Ref. [1] described 175 observables by six parameters encoding new physics and quantified the disagreement with the SM at about the $5\sigma$ level. While certain one and two parameter fits have previously been considered in detail, we establish a framework for the detailed discussion of the full 6d fit. We visualize and quantify the 6d $1\sigma$ region around the best fit point and define fit uncertainties for both current and future observables. We then define metrics quantifying the deviations between measurements and both SM and best fit predictions. These metrics relate observables to directions in parameter space, revealing their precise role in the fit, thus providing guidance for future theoretical and experimental work. Some metrics further quantify the role of correlated uncertainties, which turns out to be significant. For example the relevance of angular observables such as $P_5^\prime$ is reduced in this context. Finally, studying the space of observables allows us to discuss the internal tensions in the fit.