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→sℓ+ℓ−
transitions significant tensions between measurements and the Standard Model
predictions exist. They are most pronounced in the branching ratios ${\cal
B}_{B \to K\mu^+\mu^-}
and{\cal B}_{B_s\to\phi\mu^+\mu^-}$ (albeit quite
dependent on the form factors used) as well as in angular observables in $B\to
K^*\mu^+\mu^-
(theP_5^\prime
anomaly).Becausethemeasurementsof{\cal
B}_{B_s\to \mu^+\mu^-}
andoftheratiosR_K
andR_{K^*}$ agree reasonably
well with the SM predictions, this points towards (dominantly) lepton flavour
universal New Physics coupling vectorially to leptons, i.e. contributions to
C9U. In fact, global fits prefer this scenario over the SM hypothesis
by
5.8σ. Concerning
b→cτν 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
3σ. 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
C9U via an
off-shell penguin with the right sign and magnitude and a combined significance
(including a tree-level effect resulting in
C9μV=−C10μV and
R(D(∗))) of
6.3σ.
Such a scenario can be tested with
b→sτ+τ− decays. Finally, we
point out an interesting possible correlation of
R(D(∗)) with non-leptonic
B anomalies.