Determination of $|V_{ub}|$ from simultaneous measurements of untagged $B^0\to\pi^- \ell^+ \nu_{\ell}$ and $B^+\to\rho^0 \ell^+\nu_{\ell}$ decays

TL;DR

This paper measures the CKM matrix element |V_{ub}| by analyzing semileptonic B meson decays to pi and rho mesons using data from the Belle II detector, providing precise branching fractions and |V_{ub}| value.

Contribution

It presents a simultaneous measurement of B to pi and rho semileptonic decays without tagging partner B mesons, improving the determination of |V_{ub}| with new data and analysis methods.

Findings

Total branching fraction for B0→π−ℓ+νℓ: (1.516 ± 0.042 ± 0.059)×10^{-4}

Total branching fraction for B+→ρ0ℓ+νℓ: (1.625 ± 0.079 ± 0.180)×10^{-4}

|V_{ub}| = (3.93 ± 0.09 ± 0.13 ± 0.19)×10^{-3}

Abstract

We present a measurement of $|V_{ub}|$ from a simultaneous study of the charmless semileptonic decays $B^0\to\pi^- \ell^+ \nu_{\ell}$ and $B^+\to\rho^0 \ell^+\nu_{\ell}$, where $\ell = e, \mu$. This measurement uses a data sample of 387 million $B\overline{B}$ meson pairs recorded by the Belle~II detector at the SuperKEKB electron-positron collider between 2019 and 2022. The two decays are reconstructed without identifying the partner $B$ mesons. We simultaneously measure the differential branching fractions of $B^0\to\pi^- \ell^+ \nu_{\ell}$ and $B^+\to\rho^0 \ell^+\nu_{\ell}$ decays as functions of $q^2$ (momentum transfer squared). From these, we obtain total branching fractions $B(B^0\to\pi^- \ell^+ \nu_{\ell}) = (1.516 \pm 0.042 (\mathrm{stat}) \pm 0.059 (\mathrm{syst})) \times 10^{-4}$ and $B(B^+\to\rho^0 \ell^+\nu_{\ell}) = (1.625 \pm 0.079 (\mathrm{stat}) \pm 0.180 (\mathrm{syst})) \times 10^{-4}$. By fitting the measured $B^0\to\pi^- \ell^+ \nu_{\ell}$ partial branching fractions as functions of $q^2$, together with constraints on the non-perturbative hadronic contribution from lattice QCD calculations, we obtain $|V_{ub}|$ = $(3.93 \pm 0.09 \pm 0.13 \pm 0.19) \times 10^{-3}$. Here, the first uncertainty is statistical, the second is systematic, and the third is theoretical.