Simplification of Higher-Twist Evolution in the Large N_c Limit: Why and Why Not

TL;DR

This paper presents a simplified method for calculating the one-loop Q^2 evolution of the twist-three nucleon structure function g_T in the large-N_c limit, and explores whether similar simplifications apply to other higher-twist distributions.

Contribution

It introduces a straightforward procedure for twist-three evolution in the large-N_c limit and demonstrates that such simplifications do not extend to twist-four distributions or beyond one loop.

Findings

Simplification applies to twist-three evolution at one loop in large-N_c limit.

No similar simplification for twist-four distributions g_3, f_4, h_3.

Large-N_c simplification does not hold beyond one loop.

Abstract

Working in the light-cone gauge, we find a simple procedure to calculate the autonomous one-loop Q^2 evolution of the twist-three part of the nucleon g_T(x, Q^2) structure function in the large-N_c limit. Our approach allows us to investigate the possibility of a similar large-N_c simplification for other higher-twist evolutions. In particular, we show that it does not occur for the twist-four part of the f_4(x, Q^2), g_3(x, Q^2) and h_3(x, Q^2) distributions. We also argue that the simplification of the twist-three evolution does not persist beyond one loop.