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Observation of the decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow…
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 ${\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}}$, …