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 $\mathcal{B}(B^0\to {\pi }^{-}{\ell }^{+}{\nu }_{\ell })=(1.516\pm 0.042(\mathrm{stat})\pm 0.059(\mathrm{syst}))\times {10}^{-4}$ and $\mathcal{B}(B^{+}\to {\rho }^0{\ell }^{+}{\nu }_{\ell })=(1.625\pm 0.079(\mathrm{stat})\pm 0.180(\mathrm{syst}))\times {10}^{-4}$. By fitting the measured $B^0\to {\pi }^{-}{\ell }^{+}{\nu }_{\ell }$ partial branching fractions as functions of $q^2$, together with constraints on the nonperturbative 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.

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• Cabibbo–Kobayashi–Maskawa matrix
• Form factors
• Leptonic, semileptonic & radiative decays