Measurement of the branching fraction of the decay $B^{-}\to D^0\rho (770{)}^{-}$ at Belle II

We measure the branching fraction of the decay $B^{-}\to D^0\rho (770{)}^{-}$ using data collected with the Belle II detector. The data contain 387 million $B\bar{B}$ pairs produced in $e^{+}{e}^{-}$ collisions at the $\mathrm{{\rm Y}}(4S)$ resonance. We reconstruct $8360\pm 180$ decays from an analysis of the distributions of the $B^{-}$ energy and the $\rho (770{)}^{-}$ helicity angle. We determine the branching fraction to be $(0.939\pm 0.021(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.050(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))\mathrm{\%}$, in agreement with previous results. Our measurement improves the relative precision of the world average by more than a factor of two.