Testing Lepton Flavour Universality in $\Upsilon (4S)$ Decays

TL;DR

This paper proposes a new method using Belle II data to test Lepton Flavour Universality violations by comparing inclusive decay rates of the $S$ resonance into different lepton combinations, offering a complementary approach to existing measurements.

Contribution

It introduces a novel experimental approach to probe Lepton Flavour Universality in $b o c au u$ transitions through inclusive $S$ decay rate comparisons at Belle II.

Findings

The method relates decay rate ratios to $R(X)_{\tau\ell}$, a key LFU observable.

It demonstrates the potential to detect LFU violation signals in $S$ decays.

The approach is feasible with current Belle II capabilities.

Abstract

We propose a novel method to probe the persistent hints of Lepton Flavour Universality violation observed in semileptonic $B$ decays. Relying on the specific properties of the Belle II experiment, it consists in comparing the inclusive rates of $\Upsilon(4S) \to e^\pm \mu^\mp X$, $\Upsilon(4S) \to \mu^\pm \tau_{\rm had}^\mp X$ and $\Upsilon(4S) \to e^\pm \tau_{\rm had}^\mp X$. We show that such a measurement can be directly related to the ratio $R(X)_{\tau\ell} \equiv \Gamma (b\to X \tau \nu ) / \Gamma (b \to X \ell \nu)$ ($\ell=e$ or $\mu$), once appropriate experimental cuts are applied to suppress the effects of neutral $B$ mixing and leptons emitted through charm or tau decays. Such a measurement would thus constitute an additional and potentially competitive probe of Lepton Flavour Universality in $b\to c\ell\nu$ transitions, complementary to existing exclusive measurements, accessible in the Belle II environment.