QCD evolution of naive-time-reversal-odd parton distribution functions

TL;DR

This paper revisits the leading order QCD evolution equations for twist-3 quark-gluon correlation functions related to the Sivers and Boer-Mulders functions, clarifying discrepancies among previous derivations.

Contribution

It identifies the sources of differences in prior derivations and reconciles various results for the QCD evolution equations of these twist-3 functions.

Findings

Resolved discrepancies among previous derivations

Unified the evolution equations for $T_{q,F}(x,x)$ and $T^{(\sigma)}_{q,F}(x,x)$

Clarified the sources of differences in earlier results

Abstract

We reexamine the derivation of the leading order QCD evolution equations 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 parton distribution functions - the Sivers and Boer-Mulders function, respectively. The evolution equations were derived by several groups with apparent differences. We identify the sources that are responsible for the differences, and are able to reconcile the results from various groups.