Measurement of the Branching Fraction For the Semileptonic Decay ${D}^{0\left(+\right)}\to {\pi }^{-\left(0\right)}{\mu }^{+}{\nu }_{\mu }$ and Test of Lepton Flavor Universality

Using a data sample corresponding to an integrated luminosity of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ taken at a center-of-mass energy of 3.773 GeV with the BESIII detector operated at the BEPCII collider, we perform an analysis of the semileptonic decays ${D}^{0\left(+\right)}\to {\pi }^{-\left(0\right)}{\mu }^{+}{\nu }_{\mu }$. The branching fractions of ${D}^{0}\to {\pi }^{-}{\mu }^{+}{\nu }_{\mu }$ and ${D}^{+}\to {\pi }^{0}{\mu }^{+}{\nu }_{\mu }$ are measured to be $\left(0.272±0.00{8}_{\mathrm{stat}}±0.00{6}_{\mathrm{syst}}\right)%$ and $\left(0.350±0.01{1}_{\mathrm{stat}}±0.01{0}_{\mathrm{syst}}\right)%$, respectively, where the former is of much improved precision compared to previous results and the latter is determined for the first time. Using these results along with previous BESIII measurements of ${D}^{0\left(+\right)}\to {\pi }^{-\left(0\right)}{e}^{+}{\nu }_{e}$, we calculate the branching fraction ratios to be ${R}^{0}\equiv {B}_{{D}^{0}\to {\pi }^{-}{\mu }^{+}{\nu }_{\mu }}/{B}_{{D}^{0}\to {\pi }^{-}{e}^{+}{\nu }_{e}}=0.922±0.03{0}_{\mathrm{stat}}±0.02{2}_{\mathrm{syst}}$ and ${R}^{+}\equiv {B}_{{D}^{+}\to {\pi }^{0}{\mu }^{+}{\nu }_{\mu }}/{B}_{{D}^{+}\to {\pi }^{0}{e}^{+}{\nu }_{e}}=0.964±0.03{7}_{\mathrm{stat}}±0.02{6}_{\mathrm{syst}}$, which are compatible with the theoretical expectation of lepton flavor universality within $1.7\sigma $ and $0.5\sigma $, respectively. We also examine the branching fraction ratios in different four-momentum transfer square regions, and find no significant deviations from the standard model predictions.