NNLO QCD Corrections to $\gamma + \eta_c(\eta_b)$ Exclusive Production in Electron-Positron Collision

TL;DR

This paper calculates advanced NNLO QCD corrections for $ ext{eta}_c$ and $ ext{eta}_b$ production with a photon in electron-positron collisions, providing precise theoretical predictions for experimental tests.

Contribution

It introduces the first complete NNLO QCD correction calculations for $ ext{eta}_c$ and $ ext{eta}_b$ production in electron-positron collisions within the NRQCD framework, including novel analytic integral expressions.

Findings

Analytic expressions for master integrals using Goncharov Polylogarithms and elliptic functions.

Numerical NNLO K-factors and cross sections for BESIII and B-factory energies.

Potential tests of NRQCD higher-order predictions against experimental data.

Abstract

Based on the NRQCD factorization formalism, we calculate the next-to-next-to-leading order QCD corrections to the heavy quarkonium $\eta_c (\eta_b)$ production associated with a photon at electron-positron colliders. By matching the amplitudes calculated in full QCD theory to a series of operators in NRQCD, the short-distance coefficients up to NNLO QCD radiative corrections are determined. It turns out that the full set of master integrals that we obtained could be analytically expressed in terms of Goncharov Polylogarithms, Chen's iterated integrals, and elliptic functions, which mostly do not exist in the literature and could be employed in the analyses of other physical processes. In phenomenology, numerical calculations of NNLO K-factors and cross sections of $e^+e^-\rightarrow \gamma + \eta_c(\eta_b)$ processes in BESIII and B-factory experiments are performed, which may stand as a test of the NRQCD higher order calculation while confronting to the data.