QCD evolution of naive-time-reversal-odd quark-gluon correlation functions

TL;DR

This paper reviews and reconciles different calculations of QCD evolution kernels for twist-3 quark-gluon correlation functions related to the Sivers and Boer-Mulders functions, clarifying their scale dependence.

Contribution

It identifies and resolves discrepancies among leading-order QCD evolution kernel calculations for twist-3 quark-gluon correlators.

Findings

Discrepancies among existing kernel calculations are explained.

Results are reconciled to provide a consistent evolution framework.

Clarifies the scale dependence of naive-time-reversal-odd functions.

Abstract

In this talk, we examine the existing calculations of QCD evolution kernels for the scale dependence of two sets of twist-3 quark-gluon correlation functions, $T_{q,F}(x,x)$ and $T^{(\sigma)}_{q,F}(x,x)$, which are the first transverse-momentum-moment of the naive-time-reversal-odd Sivers and Boer-Mulders function, respectively. The evolution kernels at the leading order in strong coupling constant $\alpha_s$ were derived by several groups with apparent differences. We identify the sources of discrepancies and are able to reconcile the results from various groups.