Measurement of the Branching Fraction For the Semi-Leptonic Decays $D^{0(+)}\to {\pi }^{-(0)}{\mu }^{+}{\nu }_{\mu }$ and Test of Lepton Flavor Universality

Using a data sample corresponding to an integrated luminosity of $2.93,\rm fb^{-1}$ 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 semi-leptonic decays $D^{0(+)}\to {\pi }^{-(0)}{\mu }^{+}{\nu }_{\mu }$. The branching fractions of $D^0\to {\pi }^{-}{\mu }^{+}{\nu }_{\mu }$ and $D^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }$ are measured to be $(0.272\pm {0.008}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.006}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\mathrm{\%}$ and $(0.350\pm {0.011}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}}\pm {0.010}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}})\mathrm{\%}$, 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 $D^{0(+)}\to {\pi }^{-(0)}{e}^{+}{\nu }_e$, we calculate the branching fraction ratios to be ${\mathcal R}^0\equiv {\mathcal B}{D^{0}\to \pi^{-}\mu^+\nu\mu}/{\mathcal B}{D^{0}\to \pi^{-}e^+\nu_e}=0.922\pm 0.030{\rm stat.}\pm0.022_{\rm syst.}$and${\mathcal R}^+\equiv {\mathcal B}{D^{+}\to \pi^{0}\mu^+\nu\mu}/{\mathcal B}{D^{+}\to \pi^{0}e^+\nu_e}=0.964\pm 0.037{\rm stat.}\pm0.026_{\rm syst.}$, 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.