Precise measurements of $D^0 \to K^-\ell^+\nu_\ell$ and $D^+ \to \bar K^0\ell^+\nu_\ell$ decays

Abstract

Using $e^+e^-$ collision data corresponding to an integrated luminosity of 20.3 fb$^{-1}$, collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we present precise measurements of $D^0 \to K^-\ell^+\nu_\ell$ and $D^+ \to \bar K^0\ell^+\nu_\ell$ ($\ell=e,\mu$) decays. The branching fractions of $D^0\to K^-e^+\nu_e$, $D^0\to K^-\mu^+\nu_\mu$, $D^+\to \bar K^0e^+\nu_e$, and $D^+\to \bar K^0\mu^+\nu_\mu$ are measured to be $(3.548\pm0.006_{\rm stat}\pm0.017_{\rm syst}) \%$, $(3.445\pm0.007_{\rm stat}\pm0.017_{\rm syst}) \%$, $(8.928\pm0.025_{\rm stat}\pm0.050_{\rm syst}) \%$, and $(8.770\pm0.029_{\rm stat}\pm0.053_{\rm syst}) \%$, respectively. The partial decay rates of these four decays are measured with improved precision, and their forward-backward asymmetries are determined for the first time. By performing a simultaneous fit to the measured partial decay rates and the forward-backward asymmetries of $D \to \bar K\ell^+\nu_{\ell}$, a search for a possible scalar current contribution in the $c\to s\ell^+\nu_{\ell}$ transition is performed. The results are ${\rm Re}(c_S^{\mu})=0.017\pm0.008_{\rm stat}\pm0.006_{\rm syst}$ and ${\rm Im}(c_S^{\mu})=\pm(0.077\pm0.011_{\rm stat}\pm0.009_{\rm syst})$, corresponding to a difference from the SM with a significance of $2.3\sigma$. The product of the form factor $f_+(0)$ and the modulus of the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined to be $f_+(0)|V_{cs}|=0.7183\pm0.0007_{\rm stat}\pm0.0014_{\rm syst}$. With the inputs $|V_{cs}|=0.97349\pm0.00016$ from the Standard Model global fit or $\ffK=0.7452\pm0.0031$ from the lattice quantum chromodynamics calculation, we derive $f_+(0)=0.7383\pm0.0007_{\rm stat}\pm0.0014_{\rm syst}$ and $|V_{cs}|=0.9639\pm0.0009_{\rm stat}\pm0.0018_{\rm syst}\pm0.0040_{\rm LQCD}$.