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

TL;DR

This paper uses an effective field theory framework to analyze anomalies in B-meson decays, proposing a third-generation coupling scenario that can explain multiple anomalies simultaneously and predict rare decay rates.

Contribution

It introduces a gauge-invariant dimension-6 operator approach focusing on third-generation couplings to reconcile various B decay anomalies.

Findings

Can explain $b o s\mu^+\mu^-$ and $R(D^{(*)})$ anomalies simultaneously.

Predicts $B o K^{(*)} au\mu$ and $B_s o au\mu$ branching ratios around $10^{-6}$.

Small lepton and quark mixing angles are sufficient for the model to fit data.

Abstract

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 LHCb found 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 reexamine these decays and their correlations to $B\to K^{(*)}\nu\bar{\nu}$ 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 $b\to s\mu^+\mu^-$ 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 region of parameter space $B\to K^{(*)}\tau\mu$ and $B_s\to \tau\mu$ can be order $10^{-6}$. Possible UV completions are briefly discussed.