QCD Evolutions of Twist-3 Chirality-Odd Operators

TL;DR

This paper derives the one-loop scale evolution kernels for twist-3 chirality-odd quark-gluon distributions, highlighting differences from simpler cases and the impact of large-Nc limits.

Contribution

It provides the first explicit calculation of the scale dependence of twist-3 chirality-odd distributions using multi-parton states.

Findings

Derived the leading evolution kernel for twist-3 chirality-odd distributions.

Found that the kernel does not simplify in the large-Nc limit, unlike other twist-3 distributions.

Identified special cases where the evolution equations are simplified.

Abstract

We study the scale dependence of twist-3 distributions defined with chirality-odd quark-gluon operators. To derive the scale dependence we explicitly calculate these distributions of multi-parton states instead of a hadron. Taking one-loop corrections into account we obtain the leading evolution kernel in the most general case. In some special cases the evolutions are simplified. We observe that the obtained kernel in general does not get simplified in the large-$N_c$ limit in contrast to the case of those twist-3 distributions defined only with chirality-odd quark operators. In the later, the simplification is significant.