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LHCb reported anomalies in $B\to K^* \mu^+\mu^-$, $B_s\to\phi\mu^+\mu^-$ and$R(K)=B\to K \mu^+\mu^-/B\to K e^+e^-$. Furthermore, BaBar, BELLE and LHCbfound hints for the violation of lepton flavour universality violation in$R(D^{(*)})=B\to D^{(*)}\tau\nu/B\to D^{(*)}\ell\nu$. In this note we reexaminethese decays and their correlations to $B\to K^{(*)}\nu\bar{\nu}$ using gaugeinvariant dim-6 operators. For the numerical analysis we focus on scenarios inwhich new physics couples, in the interaction eigenbasis, to third generationquarks and lepton only. We conclude that such a setup can explain the $b\tos\mu^+\mu^-$ data simultaneously with $R(D^{(*)})$ for small mixing angles inthe lepton sector (of the order of $\pi/16$) and very small mixing angles inthe quark sector (smaller than $V_{cb}$). In these region of parameter space$B\to K^{(*)}\tau\mu$ and $B_s\to \tau\mu$ can be order $10^{-6}$. Possible UVcompletions are briefly discussed.

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

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