Test of lepton flavor universality with $\bar{B}\to D^{(\ast )}{\tau }^{-}{\bar{\nu }}_{\tau }$ and $\bar{B}\to D^{(\ast )}{\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }}$ decays at Belle II

We test lepton flavor universality with a measurement of the branching-fraction ratios $R(D^{(\ast )})\equiv \mathcal{B}(\bar{B}\to D^{(\ast )}{\tau }^{-}{\bar{\nu }}_{\tau })\mathrm{/}\mathcal{B}(\bar{B}\to D^{(\ast )}{\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }})$, where $\mathrm{\ell }$ denotes an electron or muon. The analysis uses $387\times {10}^6$ $\mathrm{{\rm Y}}(4\mathrm{S})$ decays collected with the Belle II detector in energy-asymmetric $e^{+}{e}^{-}$ collisions. One $B$ meson is fully reconstructed in a hadronic decay mode, while the other is reconstructed either in $\bar{B}\to D^{(\ast )}{\tau }^{-}{\bar{\nu }}_{\tau }$, with ${\tau }^{-}\to {\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }}{\nu }_{\tau }$, or in $\bar{B}\to D^{(\ast )}{\mathrm{\ell }}^{-}{\bar{\nu }}_{\mathrm{\ell }}$. We extract the signal from the distributions of the residual calorimeter energy and the squared mass of the undetected particles, obtaining $R(D^{\ast })=0.242\pm 0.019(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.016(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$ and $R(D)=0.439\pm 0.055(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.046(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$. These results are consistent with both the standard model predictions and previous measurements, and constitute the most precise determination of $R(D^{(\ast )})$ with hadronic tagging.