Disentangling Lepton Flavour Universal and Lepton Flavour Universality Violating Effects in $b\to s\ell^+\ell^-$ Transitions

TL;DR

This paper proposes a method to distinguish whether new physics in $b\to s\ell^+\ell^-$ transitions is mainly lepton flavour universality violating or universal, using specific observables like $Q_5$ and considering different new physics scenarios.

Contribution

It introduces a strategy to identify the nature of new physics contributions in $b\to s\ell^+\ell^-$ decays, focusing on the observable $Q_5$ and potential origins of the universal component.

Findings

$Q_5$ measurement can differentiate between LFU violating and universal effects.

A tau loop via off-shell photon penguin could generate the universal component.

$B_s\to\tau^+\tau^-$ and $B\to K^{(*)}\tau^+\tau^-$ decays are promising probes.

Abstract

In this letter we propose a strategy for discerning if new physics in the Wilson coefficient ${\cal C}_{9\mu}$ is dominantly lepton flavour universality violating or if it contains a sizable lepton flavour universal component (${\cal C}_9^{\rm U}$). Distinguishing among these two cases, for which the model independent fit of the related scenarios exhibits similar pulls w.r.t. the Standard Model, is crucial to advance our understanding of the $B$ anomalies. We first identify the origin of the degeneracy of these two cases and point out the key observables that can break it. In particular, while the observables measured so far that test lepton flavour universality exhibit similar dependencies to all the relevant Wilson coefficients, the forthcoming measurement of $Q_5=P_{5}^{\prime\mu}-P_{5}^{\prime e}$ is particularly sensitive to ${\cal C}_{9\mu}-{\cal C}_{9e}$. In fact, if $Q_5$ were found to be small (i.e. close to its Standard Model value), this would imply a small ${\cal C}_{9\mu}-{\cal C}_{9e}$ but a sizable ${\cal C}_{9}^{\rm U}$, given the preference of global fits for a large negative new physics contribution in ${\cal C}_{9\mu}$. We discuss the possible origins of ${\cal C}_9^{\rm U}$, in particular how it could originate from new physics. Here, a promising scenario, that could even link $b\to s \ell^+\ell^-$ to $R_{D^{(*)}}$, is the one in which ${\cal C}_9^{\rm U}$ is generated from a tau loop via an off-shell photon penguin diagram. This setup predicts the branching ratios of $B_s\to\tau^+\tau^-$ and $B\to K^{(*)}\tau^+\tau^-$ to lie within the reach of LHCb, CMS and Belle II. Alternatively, in case of a non-observation of these tauonic processes, we show that the most natural possibility to generate ${\cal C}_9^{\rm U}$ is a $Z^\prime$ with partially lepton flavour universal couplings.