Precise Measurement of the Chromoelectric Dipole Moment of the Charm Quark

The combined symmetry of charge conjugation and parity ($CP$) is tested in the hadronic transition $\psi(3686)\to\pi^+\pi^-J/\psi$, using a dataset of $(2712.4 \pm 14.3)\times10^{6}$ $\psi(3686)$ events collected by the BESIII detector at the BEPCII collider. The resulting asymmetry observable is $$A_{CP}=(0.6 \pm 1.8\,(\mathrm{stat}) \pm 0.1\,(\mathrm{syst}))\times10^{-4},$$ determined by combining the two channels $J/\psi\to e^+e^-$ and $J/\psi\to\mu^+\mu^-$. In addition, by considering the relationship between the chromoelectric dipole moment (CEDM) and the $A_{CP}$ observable derived from the quantum chromodynamics multipole expansion theory based on the Chen--Kuang model and the Cornell potential model, the charm-quark CEDM is determined to be $$d'_c=(2.6 \pm 7.8\,(\mathrm{stat}) \pm 0.4\,(\mathrm{syst}) \pm 0.6\,(\mathrm{theo}))\times10^{-16}\;e\,\mathrm{cm},$$ and $$d'_c=(3.5 \pm 10.5\,(\mathrm{stat}) \pm 0.6\,(\mathrm{syst}) \pm 0.5\,(\mathrm{theo}))\times10^{-16}\;e\,\mathrm{cm},$$ for the Chen--Kuang and Cornell potential models, respectively. The uncertainties are statistical, systematic, and theoretical, respectively. These results correspond to an upper limit of $$|d'_c|<2.1\times10^{-15}\;e\,\mathrm{cm}$$ at the $90\%$ confidence level, representing an order-of-magnitude improvement in sensitivity over the previous direct bound obtained using the same decay process.