Measurement of the Ratio of Partial Branching Fractions of Inclusive $\overline{B}\to X_u\ell \overline{\nu }$ to $\overline{B}\to X_c\ell \overline{\nu }$ and the Ratio of their Spectra with Hadronic Tagging

Abstract

We present a measurement of the ratio of partial branching fractions of the semi-leptonic inclusive decays, $\overline{B}\to X_u\ell \overline{\nu }$ to $\overline{B}\to X_c\ell \overline{\nu }$, where $\ell =(e,\mu )$, using the full Belle sample of $772\times 10^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance. The ratio is measured via a two-dimensional fit to the squared four-momentum transfer to the lepton pair, and the charged lepton energy in the $B$ meson rest frame, where the latter must be larger than $1$ Ge\kern -0.1em V, covering approximately $86\%$ and $78\%$ of the $\overline{B}\to X_u\ell \overline{\nu }$ and $\overline{B}\to X_c\ell \overline{\nu }$ phase space, respectively. We find $\Delta \mathcal{B}(\overline{B}\to X_u\ell \overline{\nu })/\Delta \mathcal{B}(\overline{B}\to X_c\ell \overline{\nu })=(1.99\pm 0.17_{\mathrm{stat}}\pm 0.16_{\mathrm{syst}})\times 10^{-2}$ where the uncertainties are statistical and systematic, respectively. In addition, we report the partial branching fractions separately for charged and neutral $B$ meson decays, and for electron and muon decay channels. We place a limit on isospin breaking in $\overline{B}\to X_u\ell \overline{\nu }$ decays, and find no indication of lepton flavor universality violation in either the charmed or charmless mode. Furthermore, we unfold the $\overline{B}\to X_u\ell \overline{\nu }$ and $\overline{B}\to X_c\ell \overline{\nu }$ yields and report the differential ratio in lepton energy and four-momentum transfer squared.

22 pages, 13 figures

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