The evolution of the nonsinglet twist-3 parton distribution function

TL;DR

This paper derives the leading order evolution equation for the nonsinglet twist-3 parton distribution function related to the spin-dependent structure function g2, confirming its governing dynamics in specific limits.

Contribution

It introduces a new approach to derive the evolution equation for the nonsinglet twist-3 distribution function in the non-local operator product framework.

Findings

Evolution equation for nonsinglet twist-3 distribution derived

In the limit x→1 and large N_c, evolution matches known AP equations

Confirms the governing role of AP equations in specified limits

Abstract

The twist three contributions to the $Q^2$-evolution of the spin-dependent structure function $g_2(x_{Bj},Q^2)$ are considered in the non-local operator product approach. Defining appropriate twist three distribution function we derive their evolution equation for the nonsinglet case in leading order approximation. In the limit $x_{Bj} \rightarrow 1$ as well as in the large $N_c$ limit we confirm the result that the evolution of the nonsinglet part of $g_2$ is governed by a Gribov-Lipatov-Altarelli-Parisi equation.