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

Abstract

Using a data sample corresponding to an integrated luminosity of $2.93\mathrm{f}{\mathrm{b}}^{-1}$ 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 $(0.272\pm 0.008_{stat.}\pm 0.006_{syst.})\%$ and $(0.350\pm 0.011_{stat.}\pm 0.010_{syst.})\%$, 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 ${\mathcal{R}}^0\equiv {\mathcal{B}}_{D^0\to {\pi }^{-}{\mu }^{+}{\nu }_{\mu }}/{\mathcal{B}}_{D^0\to {\pi }^{-}{e}^{+}{\nu }_e}=0.922\pm 0.030_{stat.}\pm 0.022_{syst.}$ and ${\mathcal{R}}^{+}\equiv {\mathcal{B}}_{D^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }}/{\mathcal{B}}_{D^{+}\to {\pi }^0{e}^{+}{\nu }_e}=0.964\pm 0.037_{stat.}\pm 0.026_{syst.}$, 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.

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