First Measurement of $R(X_{\tau \mathrm{/}\mathrm{\ell }})$ as an Inclusive Test of the $b\to c\tau \nu$ Anomaly

We measure the tau-to-light-lepton ratio of inclusive $B$-meson branching fractions $R(X_{\tau \mathrm{/}\mathrm{\ell }})\equiv \mathcal{B}(B\to X\tau \nu )\mathrm{/}\mathcal{B}(B\to X\mathrm{\ell }\nu )$, where $\mathrm{\ell }$ indicates an electron or muon, and thereby test the universality of charged-current weak interactions. We select events that have one fully reconstructed $B$ meson and a charged lepton candidate from $189{\mathrm{f}\mathrm{b}}^{-1}$ of electron-positron collision data collected with the Belle II detector. We find $R(X_{\tau \mathrm{/}\mathrm{\ell }})=0.228\pm 0.016(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.036(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$, in agreement with standard-model expectations. This is the first direct measurement of $R(X_{\tau \mathrm{/}\mathrm{\ell }})$.