Precision Measurement of Decay Dynamics in $D^{0(+)}\to \ddot{I}{€}^{-(0)}{\ell }^{+}\hat{I}{½}_{\ell }$

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 precisely measured, using 20.3 fb${}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The ratios of the decay widths between muon and positron channels are examined in full, across several four-momentum transfer ranges of ${\ell }^{+}\hat{I}{½}_{\ell }$. No lepton flavor universality violation is found in the current data. From a simultaneous fit to the precisely measured partial decay rates and the first measured forward-backward asymmetries of these four decays, the product of the hadronic transition form factor, $f_{+}^{D\to \ddot{I}€}(0)$, and the modulus of the $c\to d$ quark mixing element, $|V_{cd}|$, is measured with unprecedented precision to be $f_{+}^{D\to \ddot{I}€}(0)|V_{cd}|=0.1425\pm 0.0005_{stat.}\pm 0.0003_{syst.}$. Taking the value of $|V_{cd}|$ from the standard model global fit and $f_{+}^{D\to \ddot{I}€}(0)$ derived by the lattice quantum chromodynamics calculation as input, we obtain $f_{+}^{D\to \ddot{I}€}(0)=0.1425\pm 0.0005_{stat.}\pm 0.0003_{syst.}$ and $|V_{cd}|=0.2262\pm 0.0008_{stat.}\pm 0.0005_{syst.}\pm 0.0018_{LQCD.}$, respectively. The precision of each result is a factor of 2-3 better than the previous best measurements. Additionally, the real and imaginary parts of the scalar current contribution in the $c\to d{\ell }^{+}\hat{I}{½}_{\ell }$ transition are measured for the first time to be Re $(C_S^{\hat{I}}¼)=$ $0.022\pm 0.023_{stat.}\pm 0.003_{syst.}$ and $|\mathrm{Im}(C_S^{\hat{I}}¼)|=0.000\pm 0.038_{stat.}\pm 0.012_{syst.}$.

11 pages, 3 figures