Abstract In this paper, we calculate the decay widths and branching fractions for the decays Z J/ + (nS) Z → J / ψ + Υ (n S) (n=1, 2, 3 n = 1, 2, 3) at future super Z factory and at the CEPC/FCC-ee, including both the relativistic and QCD corrections within the framework of nonrelativistic QCD. Both the relativistic and QCD corrections are found to be large and negative. Compared to the leading-order results, the decay widths are significantly reduced by the higher-order corrections due to significant numerical cancellations. Despite the resulting large theoretical uncertainties, sizable event rates from these rare decay channels could still be anticipated at future high-luminosity electron-positron colliders running around the Z-pole. Ultimately, our results provide an essential theoretical baseline, highlighting the necessity of incorporating even higher-order corrections and resummation techniques for future precision phenomenological studies.
Wang et al. (Fri,) studied this question.