Review of semileptonic B anomalies

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 →s ℓ⁺ℓ^- transitions significant tensions between measurements and the Standard Model predictions exist. They are most pronounced in the branching ratios B_{B →K μ⁺μ^-} and B_{Bs→ϕμ⁺μ^-} (albeit quite dependent on the form factors used) as well as in angular observables in B →K^∗μ⁺μ^- (the P₅^' anomaly). Because the measurements of B_{Bs→μ⁺μ^-} 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 C₉^U. In fact, global fits prefer this scenario over the SM hypothesis by 5.8 σ . Concerning b →c τ ν 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 σ . 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 U₁ leptoquark or the combination of the scalar leptoquarks S₁ and S₃, leads to an effect in C₉^U via an off-shell penguin with the right sign and magnitude and a combined significance (including a tree-level effect resulting in C₉^μ=-C₁₀^μ and R (D^(∗)) ) of 6.3 σ . Such a scenario can be tested with b →s τ⁺τ^- decays. Finally, we point out an interesting possible correlation of R (D^(∗)) with non-leptonic B anomalies.