Precision measurements of semleptonic decays $D^0\to \ddot{I}{€}^{-}{\ell }^{+}\hat{I}{½}_{\ell }$ and $D^{+}\to \ddot{I}{€}^0{\ell }^{+}\hat{I}{½}_{\ell }$ ($\ell =e,\hat{I}¼$)

Abstract

The branching fractions of $D^0\to \ddot{I}{€}^{-}{e}^{+}\hat{I}{½}_e$, $D^0\to \ddot{I}{€}^{-}\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$, $D^{+}\to \ddot{I}{€}^0{e}^{+}\hat{I}{½}_e$, and $D^{+}\to \ddot{I}{€}^0\hat{I}{¼}^{+}\hat{I}{½}_{\hat{I}}¼$ are measured to be $(2.950\pm 0.017_{stat.}\pm 0.017_{syst.})\times 10^{-3}$, $(2.817\pm 0.037_{stat.}\pm 0.019_{syst.})\times 10^{-3}$, $(3.622\pm 0.034_{stat.}\pm 0.018_{syst.})\times 10^{-3}$, and $(3.507\pm 0.043_{stat.}\pm 0.026_{syst.})\times 10^{-3}$ 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 $f_{+}^{D\to \ddot{I}€}(0)$ and the modulus of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ is given by $f_{+}^{D\to \ddot{I}€}(0)|V_{cd}|=0.1425\pm 0.0005_{stat.}\pm 0.0003_{syst.}$. Taking the $|V_{cd}|$ provided by the standard model global fit and the $f_{+}^{D\to \ddot{I}€}(0)$ calculated from the lattice quantum chromodynamics as input, we obtain $f_{+}^{D\to \ddot{I}€}(0)=0.6339\pm 0.0024_{stat.}\pm 0.0014_{syst.}$ and $|V_{cd}|=0.2262\pm 0.0008_{stat.}\pm 0.0005_{syst.}\pm 0.0018_{LQCD.}$, respectively. The reported results have the best precision to date. We also search for the scalar current contribution in the $c\to d{\ell }^{+}\hat{I}{½}_{\ell }$ transition and determine Re$(C_S^{\hat{I}}¼)=$ $0.022\pm 0.023_{stat.}\pm 0.003_{syst.}$ and $|\mathrm{Im}(C_S^{\hat{I}}¼)|=0.000\pm$ $0.038_{stat.}\pm 0.012_{syst.}$. In addition, the lepton flavor universality is tested with the ratios of the decay rates between semimuonic and semielectronic decays in full and several ${\ell }^{+}\hat{I}{½}_{\ell }$ four-momentum transfer ranges.

34 pages, 17 figures