Measurement of Differential Branching Fractions of Inclusive B →x$_{u}$ℓ$^{+}$ν$_{ℓ}$ Decays

The first measurements of differential branching fractions of inclusive semileptonic B → X$_{u}$ℓ$^{+}$ν$_{ℓ}$ decays are performed using the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the Υ(4S) resonance and for ℓ=e, μ. With the availability of these measurements, new avenues for future shape-function model-independent determinations of the Cabibbo-Kobayashi Maskawa matrix element |Vx$_{ub}$| 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 → X$_{u}$ℓ$^{+}$ν$_{ℓ}$ decays and other processes, and corrected for resolution and acceptance effects.