$B$ Flavour Anomalies: 2021 Theoretical Status Report

Abstract

At the present time, there are discrepancies with the predictions of the SM in several observables involving $b\to s{\ell }^{+}{\ell }^{-}$ and $b\to c{\ell }^{-}{\bar{\nu }}_{\ell }$ decays. These are the $B$ flavour anomalies. In this review, we summarize the data as of Moriond 2021 and present theoretical new-physics explanations from both a model-independent effective-field-theory point of view and through the building of explicit models. Throughout, we stress the complementarity of these two approaches. We also discuss combined explanations of both $B$ anomalies, and present models that also explain other problems, such as dark matter, $(g-2{)}_{\mu }$, neutrino properties, and hadronic anomalies.

Comments: 48 pages, 1 figure. To be published in the Annual Review of Nuclear and Particle Science. Changes: minor modifications of the text, references updated and added