Observation of the decay D0→ρ−μ+νμ

By analyzing an ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data sample corresponding to an integrated luminosity of $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure the branching fraction of the ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ decay for the first time. We obtain ${\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}=(1.35\ifmmode\pm\else\textpm\fi{}{0.09}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}{0.09}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. Using the world average of ${\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}}$, we find a branching fraction ratio of ${\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}/{\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}}=0.90\ifmmode\pm\else\textpm\fi{}0.11$, which agrees with the theoretical expectation of lepton flavor universality within the uncertainty. Combining the world average of ${\mathcal{B}}_{{D}^{+}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}$ and the lifetimes of ${D}^{0(+)}$, we obtain a partial decay width ratio of ${\mathrm{\ensuremath{\Gamma}}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}/(2{\mathrm{\ensuremath{\Gamma}}}_{{D}^{+}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}})=0.71\ifmmode\pm\else\textpm\fi{}0.14$, which is consistent with the isospin symmetry expectation of unity within $2.1\ensuremath{\sigma}$. For the reported values of ${\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}/{\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}/2{\mathrm{\ensuremath{\Gamma}}}_{{D}^{+}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}}$, the uncertainty is the quadratic sum of the statistical and systematic uncertainties.