Measurement of Differential Branching Fractions of Inclusive ${B to X_u , ell^+, u_{ell}}$ Decays

The first measurements of differential branching fractions of inclusive semileptonic ${B to X_u , ell^+, u_{ell}}$ decays are performed using the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the $Upsilon(4S)$ resonance and for $ell = e, mu$. Differential branching fractions are reported as a function of the lepton momentum, 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 ${B to X_c , ell^+, u_{ell}}$ decays and other processes, and corrected for resolution and acceptance effects. The measured distributions are compared to predictions from inclusive and hybrid ${B to X_u , ell^+, u_{ell}}$ calculations.