Measurement of inclusive $B \to X_u \ell \nu$ partial branching fractions and $|V_{ub}|$ at Belle II

A sample of 365 fb$^{-1}$ of $e^+e^- \to \Upsilon(4S) \to B\bar{B}$ data collected by the Belle II experiment is used to measure the partial branching fractions of charmless semileptonic $B$ meson decays and determine the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$. Events containing a signal electron or muon $\ell$ and a fully reconstructed hadronic $B$ decay that constrains the signal kinematics are selected, while the rest of the event defines the hadronic system $X_u$ associated with the signal. To discriminate the signal from the 50-times larger background originating from CKM-favored semileptonic $B$ decays, a template fit is performed in both signal and control regions after applying an optimized selection. The partial branching fraction measured for lepton energies greater than 1 GeV in the signal $B$ meson rest frame is $\Delta\mathcal{B}(B \to X_u \ell \nu) = (1.54 \pm 0.08 \, {\rm (stat.)} \pm 0.12 \, {\rm (syst.)}) \times 10^{-3}$. From this measurement, using the Gambino, Giordano, Ossola, Uraltsev theoretical framework, $|V_{ub}| = (4.01 \pm 0.19 ^{+0.07} _{-0.08}) \times 10^{-3}$ is determined, where the uncertainties are experimental and theoretical, respectively. This value is consistent with the world average obtained from previous inclusive measurements. Different theoretical predictions and partial branching fractions measured in other phase-space regions, defined by additional selections on the $X_u$ and leptonic system masses, are also used to determine $|V_{ub}|$.