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We propose a novel method to probe the persistent hints of Lepton FlavourUniversality violation observed in semileptonic $B$ decays. Relying on thespecific properties of the Belle II experiment, it consists in comparing theinclusive rates of $\Upsilon(4S) \to e^\pm \mu^\mp X$, $\Upsilon(4S) \to\mu^\pm \tau_{\rm had}^\mp X$ and $\Upsilon(4S) \to e^\pm \tau_{\rm had}^\mpX$. 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 suppressthe effects of neutral $B$ mixing and leptons emitted through charm or taudecays. Such a measurement would thus constitute an additional and potentiallycompetitive probe of Lepton Flavour Universality in $b\to c\ell\nu$transitions, complementary to existing exclusive measurements, accessible inthe Belle II environment.

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