Testing Lepton Flavour Universality in ${\rm Y}(4S)$ Decays

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 ${\rm Y}(4S)\to e^{\pm }{\mu }^{\mp }X$, ${\rm Y}(4S)\to {\mu }^{\pm }{\tau }_{\mathrm{had}}^{\mp }X$ and ${\rm Y}(4S)\to e^{\pm }{\tau }_{\mathrm{had}}^{\mp }X$. 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.

Comments: 8 pages, 1 figure