Measurement of the ratio of partial branching fractions of inclusive B ¯ →xuℓ ν ¯ to B ¯ →xcℓ ν ¯ and the ratio of their spectra with hadronic tagging

We present a measurement of the ratio of partial branching fractions of the semileptonic inclusive decays, B¯→Xuℓν¯ to B¯→Xcℓν¯, where ℓ=(e,μ), using the full Belle sample of 772×106 BB¯ pairs collected at the ϒ(4S) resonance. The identification of inclusive B¯→Xuℓν¯ decays is difficult due to the abundance of Cabibbo-Kobayashi-Maskawa-favored B¯→Xcℓν¯ events, which share a similar event topology. To minimize dependence on the modeling of these channels, a data-driven description of B¯→Xcℓν¯ is employed. 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 GeV, covering approximately 86% and 78% of the B¯→Xuℓν¯ and B¯→Xcℓν¯ phase space, respectively. We find ΔB(B¯→Xuℓν¯)/ΔB(B¯→Xcℓν¯)=(1.99±0.17stat±0.16syst)×10-2, where the uncertainties are statistical and systematic, respectively. We extract |Vub|/|Vcb| using two theoretical calculations for the partial decay rate of B¯→Xuℓν¯, finding (|Vub|/|Vcb|)BLNP=(9.81±0.42stat±0.38syst±0.51ΔΓ(B¯→Xuℓν¯)±0.20ΔΓ(B¯→Xcℓν¯))×10-2 and (|Vub|/|Vcb|)GGOU=(10.06±0.43stat±0.39syst±0.23ΔΓ(B¯→Xuℓν¯)±0.20ΔΓ(B¯→Xcℓν¯))×10-2, where the third and fourth uncertainties are from the partial decay rates of B¯→Xuℓν¯ and B¯→Xcℓν¯, 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 B¯→Xuℓν¯ decays, and find no indication of lepton flavor universality violation in either the charmed or charmless mode. Furthermore, we unfold the B¯→Xuℓν¯ and B¯→Xcℓν¯ yields and report the differential ratio in lepton energy and four-momentum transfer squared.