A note on the scale evolution of the ETQS function T_F(x,x)

TL;DR

This paper clarifies the scale evolution of the ETQS twist-3 matrix element by resolving previous conflicting results through careful treatment of methodological subtleties.

Contribution

It demonstrates that the results of one prior study can be reproduced with improved care, resolving discrepancies in the understanding of ETQS function's scale dependence.

Findings

Reproduced results of Ref.[4] with careful treatment

Resolved conflicts among previous studies

Enhanced understanding of ETQS scale evolution

Abstract

We reexamine the scale dependence of the ETQS (Efremov-Teryaev-Qiu-Sterman) twist-3 matrix element which has been studied already by the four different groups with conflicting results Ref.[1-4]. We find that we can in fact reproduce the results of Ref.[4] with the method Ref.[4] when we treat some subtleties with greater care, thus easing the mentioned conflict.