Resummation of relativistic corrections to heavy quarkonium $+\,\gamma$ production at $Z$ factory

TL;DR

This paper calculates the production cross sections of heavy quarkonium plus a photon at the Z boson resonance, including relativistic corrections within NRQCD, revealing significant effects for charmonium but negligible for bottomonium.

Contribution

It provides the first resummed relativistic correction calculations for heavy quarkonium production at the Z factory within the NRQCD framework.

Findings

Relativistic corrections reduce charmonium production cross sections by 20-30%.

Relativistic effects on bottomonium are negligible, under 2%.

Results include vector-meson-dominance approach for J/psi and Upsilon.

Abstract

Cross sections of the heavy quarkonium production process $e^+e^-\to H + \gamma$ at the c.m. energy of $Z^0$-boson resonance are calculated at leading order in $\alpha_s$ with relativistic corrections resummed within the framework of nonrelativistic QCD (NRQCD). $S$- and $P$-wave charmonia and bottomonia are considered. For $J/\psi(\Upsilon)$ production, the result of vector-meson-dominance (VMD) approach is also given. Relativistic contributions to charmonium production are of the same magnitude as next-to-leading order QCD corrections, decreasing cross section 20-30%. Relativistic corrections to bottomonium production are negligible, not exceeding 2%.