Precision Measurement of Decay Dynamics in $D^{0(+)}\to π^{-(0)}\ell^+ν_\ell$

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 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 $\ell^+ν_{\ell}$. 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, $f^{D\toπ}_+(0)$, and the modulus of the $c\to d$ quark mixing element, $|V_{cd}|$, is measured with unprecedented precision to be $f^{D\toπ}_+(0)|V_{cd}|=0.1425\pm0.0005_{\rm stat.}\pm0.0003_{\rm syst.}$. Taking the value of $|V_{cd}|$ from the standard model global fit and $f^{D\toπ}_+(0)$ derived by the lattice quantum chromodynamics calculation as input, we obtain $f^{D\toπ}_+(0)=0.1425\pm0.0005_{\rm stat.}\pm0.0003_{\rm syst.}$ and $|V_{cd}|=0.2262\pm0.0008_{\rm stat.}\pm0.0005_{\rm syst.}\pm0.0018_{\rm LQCD.}$, 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 $c\to d \ell^+ν_{\ell}$ transition are measured for the first time to be Re $(C_S^μ)=$ $0.022 \pm 0.023_{\rm stat.}\pm 0.003_{\rm syst.}$ and $|\mathrm{Im} (C_S^μ)|=0.000 \pm 0.038_{\rm stat.}\pm 0.012_{\rm syst.}$.