Scale Dependence of Twist-3 Quark-Gluon Operators for Single Spin Asymmetries

TL;DR

This paper derives the one-loop scale dependence of twist-3 quark-gluon operators, crucial for understanding transverse single spin asymmetries, and compares the results with existing findings for soft-gluon-pole matrix elements.

Contribution

It provides the first derivation of the one-loop scale evolution equations for twist-3 quark-gluon operators, including special cases relevant to single spin asymmetries.

Findings

Derived the scale dependence of twist-3 operators at one-loop.

Obtained evolution equations for soft-gluon-pole and soft-quark-pole matrix elements.

Compared new results with existing literature on soft-gluon-pole matrix elements.

Abstract

We derive the scale dependence of twist-3 quark-gluon operators, or ETQS matrix elements, at one-loop. These operators are used to factorize transverse single spin asymmetries, which are studied intensively both in experiment and theory. The scale dependence of two special cases are particularly interesting. One is of soft-gluon-pole matrix elements, another is of soft-quark-pole matrix elements. From our results the evolutions in the two cases can be obtained. A comparison with existing results of soft-gluon-pole matrix elements is made.