Precision measurements of semleptonic decays $D^0 \to π^-\ell^+ν_\ell$ and $D^+ \to π^0\ell^+ν_\ell$ ($\ell =e,μ$)

Abstract

The branching fractions of $D^0\to π^-e^+ν_e$, $D^0\to π^-μ^+ν_μ$, $D^+\to π^0e^+ν_e$, and $D^+\to π^0μ^+ν_μ$ are measured to be $(2.950\pm0.017_{\rm stat.}\pm 0.017_{\rm syst.})\times10^{-3}$, $(2.817\pm0.037_{\rm stat.}\pm 0.019_{\rm syst.})\times10^{-3}$, $(3.622\pm0.034_{\rm stat.}\pm 0.018_{\rm syst.})\times10^{-3}$, and $(3.507\pm0.043_{\rm stat.}\pm 0.026_{\rm syst.})\times10^{-3}$ using $e^+e^-$ collision data with an integrated luminosity of 20.3 fb$^{-1}$ collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The partial decay rates of these four decays are measured with the best precision to date and their forward-backward asymmetries are determined for the first time. By performing a simultaneous fit to these results, the product of the hadronic transition form factor $f^{D\toπ}_+(0)$ and the modulus of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ is given by $f^{D\toπ}_+(0)|V_{cd}|=0.1425\pm0.0005_{\rm stat.}\pm0.0003_{\rm syst.}$. Taking the $|V_{cd}|$ provided by the standard model global fit and the $f^{D\toπ}_+(0)$ calculated from the lattice quantum chromodynamics as input, we obtain $f^{D\toπ}_+(0)=0.6339\pm0.0024_{\rm stat.}\pm0.0014_{\rm syst.}$ and $|V_{cd}|=0.2262\pm0.0008_{\rm stat.}\pm0.0005_{\rm syst.}\pm0.0018_{\rm LQCD.}$, respectively. The reported results have the best precision to date. We also search for the scalar current contribution in the $c\to d \ell^+ν_{\ell}$ transition and determine Re$(C_S^μ)=$ $0.022 \pm 0.023_{\rm stat.}\pm 0.003_{\rm syst.}$ and $|{\rm Im}(C_S^μ)|=0.000 \pm $ $0.038_{\rm stat.} \pm 0.012_{\rm syst.}$. In addition, the lepton flavor universality is tested with the ratios of the decay rates between semimuonic and semielectronic decays in full and several $\ell^+ν_\ell$ four-momentum transfer ranges.