Large-order trend of the anomalous-dimensions spectrum of trilinear twist-3 quark operators

TL;DR

This paper computes the anomalous dimensions of twist-3 trilinear quark operators at leading order, revealing a logarithmic asymptotic trend in their spectrum through analytical and numerical methods.

Contribution

It introduces a combined analytical and numerical approach to calculate high-order anomalous dimensions of twist-3 quark operators using Appell polynomial basis.

Findings

Anomalous dimensions form a degenerate spectrum.

Upper envelope of the spectrum exhibits logarithmic growth.

Method enables calculations up to order 400.

Abstract

The anomalous dimensions of trilinear-quark operators are calculated at leading twist $t=3$ by diagonalizing the one-gluon exchange kernel of the renormalization-group type evolution equation for the nucleon distribution amplitude. This is done within a symmetrized basis of Appell polynomials of maximum degree $M$ for $M\gg 1$ (up to order 400) by combining analytical and numerical algorithms. The calculated anomalous dimensions form a degenerate system, whose upper envelope shows asymptotically logarithmic behavior.