Two-loop $O(\epsilon)$ term of $1/(mr^2)$ heavy quarkonium potential

TL;DR

This paper computes the two-loop $O(psilon)$ correction to the $1/(mr^2)$ potential in heavy quarkonium, refining previous results and analyzing color factor coefficients for improved theoretical accuracy.

Contribution

It provides the first detailed calculation of the two-loop $O(psilon)$ term for the heavy quarkonium potential, including a careful examination of color factors.

Findings

Small difference found in the color factor coefficient compared to previous work

Refined calculation enhances the precision of heavy quarkonium potential models

Analysis of color factors improves understanding of non-abelian contributions

Abstract

As a straightforward application of the recently calculated two-loop heavy quarkonium Hamiltonian, we evaluate the two-loop $O(\epsilon)$ term of the $1/(mr^2)$ heavy quarkonium potential. Compared to a previous calculation we find a small difference in the coefficient of the maximally non-abelian color factor $C_F C_A^2 $. We further examine this coefficient carefully.