We propose a novel method to probe the persistent hints of lepton flavor 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 $\mathrm{\Upsilon }(4S)\to e^{\pm }{\mu }^{\mp }X$, $\mathrm{\Upsilon }(4S)\to {\mu }^{\pm }{\tau }_{\mathrm{had}}^{\mp }X$ and $\mathrm{\Upsilon }(4S)\to e^{\pm }{\tau }_{\mathrm{had}}^{\mp }X$. We show that such a measurement can be directly related to the ratio $R(X{)}_{\tau \ell }\equiv \mathrm{\Gamma }(B\to X\tau \nu )/\mathrm{\Gamma }(B\to X\ell \nu )$ ($\ell =e$ 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 flavor universality in $b\to c\ell \nu$ transitions, complementary to existing exclusive measurements, accessible in the Belle II environment.

• Received 30 April 2021
• Accepted 24 May 2021

DOI:https://doi.org/10.1103/PhysRevD.103.113009

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Published by the American Physical Society