Effective Field Theory Approach to b → sll(1), B → K(*) ν(ν)over-bar and B → D(*)τν with Third Generation Couplings

The LHCb Collaboration reported anomalies in B -> K*mu(+)mu(-), B-s -> phi mu(+)mu(-), and R(K) = B -> K mu(+)mu(-)/B -> Ke(+)e(-). Furthermore, BABAR, BELLE, and LHCb Collaborations found hints for the violation of lepton-flavor universality violation in R(D-(*)) = B -> D-(*) t nu/B -> D-(*) l nu. In this Letter we reexamine these decays and their correlations to B -> K-(*) nu(nu) over bar 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 -> s mu(+)mu-data simultaneously with R(D-(*)) for small mixing angles in the lepton sector (of the order of pi/16) and very small mixing angles in the quark sector (smaller than V-cb). In these regions of parameter space, B -> K-(*)tau mu and B-s -> tau mu can be order 10(-6). Possible UV completions are briefly discussed.