The first measurements of differential branching fractions of inclusive semileptonic $B\to X_u{\ell }^{+}{\nu }_{\ell }$ decays are performed using the full Belle data set of $711{\mathrm{fb}}^{-1}$ of integrated luminosity at the $\mathrm{\Upsilon }(4S)$ resonance and for $\ell =e$, $\mu$. With the availability of these measurements, new avenues for future shape-function model-independent determinations of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ub}|$ can be pursued to gain new insights in the existing tension with respect to exclusive determinations. The differential branching fractions are reported as a function of the lepton energy, the four-momentum-transfer squared, light-cone momenta, the hadronic mass, and the hadronic mass squared. They are obtained by subtracting the backgrounds from semileptonic $B\to X_c{\ell }^{+}{\nu }_{\ell }$ decays and other processes, and corrected for resolution and acceptance effects.

• Received 29 July 2021
• Accepted 9 November 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.261801

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Published by the American Physical Society