Observation of the decay ${D}^{0}\to {\rho }^{-}{\mu }^{+}{\nu }_{\mu }$

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