Effective Field Theory Approach to b→sℓℓ^{(')}, B→K^{(*)}νν[over ¯] and B→D^{(*)}τν with Third Generation Couplings

The LHCb Collaboration reported anomalies in B→K^{*}μ^{+}μ^{-}, B_{s}→ϕμ^{+}μ^{-}, and R(K)=B→Kμ^{+}μ^{-}/B→Ke^{+}e^{-}. Furthermore, BABAR, BELLE, and LHCb Collaborations found hints for the violation of lepton-flavor universality violation in R(D^{(*)})=B→D^{(*)}τν/B→D^{(*)}ℓν. In this Letter we reexamine these decays and their correlations to B→K^{(*)}νν[over ¯] using gauge invariant dim-6 operators. For the numerical analysis we focus on scenarios in which new physics couples, in the interaction eigenbasis, to third generation quarks and lepton only. We conclude that such a setup can explain the b→sμ^{+}μ^{-} data simultaneously with R(D^{(*)}) for small mixing angles in the lepton sector (of the order of π/16) and very small mixing angles in the quark sector (smaller than V_{cb}). In these regions of parameter space, B→K^{(*)}τμ and B_{s}→τμ can be order 10^{-6}. Possible UV completions are briefly discussed.