Precise Measurement of Chromo-Electric Dipole Moment of the Charm Quark

The combined symmetry of charge conjugation and parity ($C\text{\hspace{0.17em}⁣}P$) is tested in the hadronic transition $\psi (3686)\to {\pi }^{+}{\pi }^{-}J\mathrm{/}\psi$, utilizing a dataset of 2.7 billion $\psi (3686)$ events collected by the BESIII detector at the BEPCII collider. The resulting asymmetry observable is $A_{cp}=(0.6\pm {1.8}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.1}_{\mathrm{s}\mathrm{y}\mathrm{s}})\times {10}^{-4}$ by combining the two channels $J\mathrm{/}\psi \to e^{+}{e}^{-}$ and $J\mathrm{/}\psi \to {\mu }^{+}{\mu }^{-}$ with unprecedented precision. Meanwhile, by considering the relationship between the chromo-electric dipole moment (CEDM) and the $A_{cp}$ observable derived from the quantum chromo-dynamics multipole expansion (QCDME) theory based on Chen-Kuang, as well as Cornell potential model, we yield the results of charm quark’s CEDM with $d_c^{\mathrm{\prime }}=(2.6\pm {7.8}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.4}_{\mathrm{s}\mathrm{y}\mathrm{s}}\pm {0.6}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}})\times {10}^{-16}$ $e\cdot$cm, and $d_c^{\mathrm{\prime }}=(3.5\pm {10.5}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.6}_{\mathrm{s}\mathrm{y}\mathrm{s}}\pm {0.5}_{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}})\times {10}^{-16}$ $e\cdot$cm, respectively. These results correspond to an upper limit of $\mathrm{\mid }{d}_c^{\mathrm{\prime }}\mathrm{\mid }<2.1\times {10}^{-15}e\cdot$cm at a 90% confidence level, an order of magnitude improvement in sensitivity compared to the previous direct bound using the same decay process. Our results provide insights into the dynamics of charmonium hadronic transitions, shedding light on their behavior in the context of $C\text{\hspace{0.17em}⁣}P$ violation.