Determination of $|V_{ub}|$ from simultaneous measurements of untagged $B^0\to \ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ and $B^{+}\to \ddot{I}{}^0{\ell }^{+}\hat{I}{½}_{\ell }$ decays

Abstract

We present a measurement of $|V_{ub}|$ from a simultaneous study of the charmless semileptonic decays $B^0\to \ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ and $B^{+}\to \ddot{I}{}^0{\ell }^{+}\hat{I}{½}_{\ell }$, where $\ell =e,\hat{I}¼$. 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 $B^0\to \ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ and $B^{+}\to \ddot{I}{}^0{\ell }^{+}\hat{I}{½}_{\ell }$ decays as functions of $q^2$ (momentum transfer squared). From these, we obtain total branching fractions $B(B^0\to \ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell })=(1.516\pm 0.042(\mathrm{stat})\pm 0.059(\mathrm{syst}))\times 10^{-4}$ and $B(B^{+}\to \ddot{I}{}^0{\ell }^{+}\hat{I}{½}_{\ell })=(1.625\pm 0.079(\mathrm{stat})\pm 0.180(\mathrm{syst}))\times 10^{-4}$. By fitting the measured $B^0\to \ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ 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.