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

Abstract

LHCb reported anomalies in $B\to K^* μ^+μ^-$, $B_s\toϕμ^+μ^-$ and $R(K)=B\to K μ^+μ^-/B\to K e^+e^-$. Furthermore, BaBar, BELLE and LHCb found hints for the violation of lepton flavour universality violation in $R(D^{(*)})=B\to D^{(*)}τν/B\to D^{(*)}\ellν$. In this note we reexamine these decays and their correlations to $B\to K^{(*)}ν\barν$ 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 $b\to sμ^+μ^-$ 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 region of parameter space $B\to K^{(*)}τμ$ and $B_s\to τμ$ can be order $10^{-6}$. Possible UV completions are briefly discussed.