Higher Order Corrections to the Cross Section of e+e- to Quarkonium plus gamma

TL;DR

This paper calculates higher order QCD and relativistic corrections to the production cross section of heavy quarkonium plus a photon in electron-positron collisions, revealing significant effects on the cross section estimates.

Contribution

It provides analytical expressions for NLO QCD radiative and relativistic corrections within NRQCD for quarkonium plus photon production.

Findings

Radiative and relativistic corrections are substantial.

Analytical formulas for NLO corrections are derived.

Cross section estimates are significantly affected by these corrections.

Abstract

The production cross sections of $e^+e^- $ to a heavy quarkonium with $C$-parity even $S-$wave and $P-$wave associated with a photon are analyzed in the framework of non-relativistic Quantum Chromodynamics(NRQCD) factorization formalism. The short-distance coefficients are determined up to the next-to-leading order(NLO) QCD radiative corrections for $S-$ and $P-$wave and NLO relativistic corrections for $S-$wave in analytical forms. Applying the results to estimate the cross sections we find that both the radiative and relativistic corrections are considerable.