Review of semileptonic B anomalies

Abstract

We review the current status and implications of the anomalies (i.e. deviations from the Standard Model predictions) in semi-leptonic B meson decays, both in the charged and in the neutral current. In $b\rightarrow s\ell ^+\ell ^-$ transitions significant tensions between measurements and the Standard Model predictions exist. They are most pronounced in the branching ratios ${{\mathcal {B}}}_{B \rightarrow K\mu ^+\mu ^-}$ and ${{\mathcal {B}}}_{B_s\rightarrow \phi \mu ^+\mu ^-}$ (albeit quite dependent on the form factors used) as well as in angular observables in $B\rightarrow K^*\mu ^+\mu ^-$ (the $P_5^\prime$ anomaly). Because the measurements of ${{\mathcal {B}}}_{B_s\rightarrow \mu ^+\mu ^-}$ and of the ratios R(K) and $R(K^*)$ agree reasonably well with the SM predictions, this points towards (dominantly) lepton flavour universal NP coupling vectorially to leptons, i.e. contributions to $C_9^{\textrm{U}}$. In fact, global fits prefer this scenario over the SM hypothesis by $5.8\sigma$. Concerning $b\rightarrow c\tau \nu$ transitions, R(D) and $R(D^*)$ suggest constructive new physics at the level of $10\%$ (w.r.t. the Standard Model amplitude) with a significance above $3\sigma$. We discuss new physics explanations of both anomalies separately as well as possible combined explanations. In particular, a left-handed vector current solution to $R(D^{(*)})$, either via the $U_1$ leptoquark or the combination of the scalar leptoquarks $S_1$ and $S_3$, leads to an effect in $C_9^{\textrm{U}}$ via an off-shell penguin with the right sign and magnitude and a combined significance (including a tree-level effect resulting in $C_9^\mu =-C_{10}^\mu$ and $R(D^{(*)})$) of $6.3\sigma$. Such a scenario can be tested with $b \rightarrow s \tau ^+\tau ^-$ decays. Finally, we point out an interesting possible correlation of $R(D^{(*)})$ with non-leptonic B anomalies.