Next-to-leading order QCD and relativistic corrections to $Z \to J/\psi+\Upsilon(nS)$

TL;DR

This paper calculates the decay widths and branching fractions of Z boson decays into J/ψ and Υ states, incorporating significant relativistic and QCD corrections within nonrelativistic QCD, crucial for accurate predictions at future colliders.

Contribution

It provides the first comprehensive calculation of these decay channels including both relativistic and QCD corrections, showing their large negative impact on decay widths.

Findings

Relativistic and QCD corrections significantly reduce decay widths.

Higher-order corrections are essential for reliable estimates.

Potential for sizable event rates at future high-luminosity colliders.

Abstract

In this paper, we calculate the decay widths and branching fractions for the decays $Z \to J/\psi+\Upsilon(nS)$ ($n=1,2,3$) 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. Therefore, it is essential to take these corrections into account for a reliable estimation. For a high-luminosity electron positron collider running around the $Z$-pole, sizable event rates could be produced from these rare decay channels due to the $Z$-boson resonance effect.