Effective field theory approach to $b\to s\ell\ell^{(\prime)}$, $B\to K^{(*)}��\bar��$ and $B\to D^{(*)}����$ with third generation couplings

LHCb reported anomalies in $B\to K^* ��^+��^-$, $B_s\to����^+��^-$ and $R(K)=B\to K ��^+��^-/B\to K e^+e^-$. Furthermore, BaBar, BELLE and LHCb found hints for the violation of lepton flavour universality violation in $R(D^{(*)})=B\to D^{(*)}����/B\to D^{(*)}\ell��$. In this note we reexamine these decays and their correlations to $B\to K^{(*)}��\bar��$ 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 $b\to s��^+��^-$ data simultaneously with $R(D^{(*)})$ for small mixing angles in the lepton sector (of the order of $��/16$) and very small mixing angles in the quark sector (smaller than $V_{cb}$). In these region of parameter space $B\to K^{(*)}����$ and $B_s\to ����$ can be order $10^{-6}$. Possible UV completions are briefly discussed.

7 pages, 3 figures