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

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

Figure 1

Fits to the $M_{\mathrm{BC}}$ distributions of the ST ${\overline{D}}^0$ (left column) and $D^{-}$ (middle and right columns) modes. The dots with error bars are data. The blue solid and red dashed curves are the fit results and the fitted backgrounds. The signal region is between the red arrows.

Figure 2

Fits to the $M_{\mathrm{miss}}^2$ distributions of the DT candidates. The dots with error bars are data. The blue solid, green long dashed, pink dashed, red dotted and black dot-dashed curves represent the overall fit results, the SL signals, the BKGI, BKGII and BKGIII components (see text), respectively.

Figure 3

$\mathrm{\Delta }{\mathrm{\Gamma }}_i^{0(+)}/\mathrm{\Delta }{q}^2$ of $D^{0(+)}\to {\pi }^{-(0)}{\ell }^{+}{\nu }_{\ell }$ (top) and ${\mathcal{R}}_{\mathrm{LFU}}^{0(+)}$ (bottom) in various $q^2$ bins. The calculations of $\mathrm{\Delta }{\mathrm{\Gamma }}_{\mathrm{i}}^{0(+)}/\mathrm{\Delta }{q}^2$ of $D^{0(+)}\to {\pi }^{-(0)}{e}^{+}{\nu }_e$ are quoted from Refs. [15, 16]. Data are shown as dots with error bars, where the uncertainties are combined from statistical and systematic errors, and the uncertainties in ${\mathcal{R}}_{\mathrm{LFU}}^{0(+)}$ are dominated by the statistical uncertainties of semi-muonic modes. The blue, green and black curves with bands show the LQCD predictions with uncertainties, using the equations and HFF parameters described in Refs. [19, 38], where the theoretical uncertainties in ${\mathcal{R}}_{\mathrm{LFU}}^{0(+)}$ are tiny due to strong correlation of the form factors.