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

TL;DR

This study reports a Belle II measurement of inclusive charmless semileptonic B decays, extracting partial branching fractions in three phase-space regions defined by $E_ ext{ℓ}^B$, $M_X$, and $q^2$ using hadronic tagging to constrain signal kinematics. The analysis employs HQE-based frameworks (BLNP, DGE, GGOU) to derive $|V_{ub}|$ from the measured $rac{Δ ext{B}(B o X_u ilde{ u} ilde{ℓ})}{ ilde{Γ}(B o X_u ilde{ℓ} ilde{ν})}$ relation, including data-driven continuum and $B o X_c ilde{ℓ} ilde{ν}$ background corrections. Three measurements of $Δ ext{B}(B o X_u ilde{ℓ} ilde{ν})$ yield consistent $|V_{ub}|$ values across regions, with the broadest region giving the most precise result $|V_{ub}| = (4.01^{+0.07}_{-0.08} ext{(theory)}) imes 10^{-3}$ (GGOU) when combined with the partial decay rate. The results are compatible with the inclusive world average and offer a cross-check against exclusive determinations, contributing to the resolution of the $|V_{ub}|$ puzzle and providing a benchmark for HQE-based predictions in semileptonic $B$ decays.

Abstract

A sample of 365 fb$^{-1}$ of $e^+e^- \to Υ(4S) \to B\bar{B}$ 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 $Δ\mathcal{B}(B \to X_u \ell ν) = (1.54 \pm 0.08 \, {\rm (stat.)} \pm 0.12 \, {\rm (syst.)}) \times 10^{-3}$. 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 $|V_{ub}|$.

Figures (10)

• Figure 1: Feynman diagram of the leading $B \rightarrow X_u \ell \nu$ transition. The $X_u$ system can either represent a specific meson or a non-resonant system comprising several hadrons produced by the fragmentation of the $u\bar{q}$ system.
• Figure 2: $B \rightarrow X_c \ell \nu$ suppression classifier output score. Simulated templates are shown as stacked histograms and experimental data are shown as black points. The signal component is shown as a purple line with its yield multiplied by 10 to enhance visibility. The bottom panel shows the ratio between data and simulation yields in each bin. The purple arrows indicate that the point is outside of the plotting range and the purple crosses indicate the absence of simulated data in a particular bin. The step in the distribution in the range $0.70-0.75$ is caused by the large number of events with a $p_{\rm vtx}^{\rm ROE}$ close to zero (see Figure \ref{['fig:xclnu_mva_input']} in Appendix \ref{['app:xclnu_suppression']}).
• Figure 3: Distribution of $C_1$ (first CLEO cone CLEO:1995rok) in an off-resonance sample before (left) and after (right) the continuum modeling correction is applied. The modeling uncertainties, described in Section \ref{['sec:cont_calibration_error']}, are included in the error band after applying the continuum calibration. The bottom panel shows the ratio between data and simulation yields in each bin. The purple arrows indicate that the point is outside of the plotting range and the purple crosses indicate the absence of simulated data in a particular bin.
• Figure 4: The data samples after reconstruction, preselection and continuum suppression are subdivided into six regions illustrated here. The selection plane is subdivided based on the kaon multiplicity (vertical axis) and the $B \rightarrow X_c \ell \nu$ suppression classifier score (horizontal axis). The signal and control regions used for the signal extraction are highlighted in green and purple, respectively.
• Figure 5: $E_{\ell}^B$, $M_X$ and $q^2$ distributions in data and simulation in the CR$_{0, \mathrm{low}}$ region defined in the text. Only the $E_{\ell}^B > 1$ GeV kinematic selection is applied. All systematic uncertainties as described in Section \ref{['sec:syst_uncert']} are included. The bottom panel shows the ratio between data and simulation yields in each bin. The purple arrows indicate that the point is outside of the plotting range.