On scale dependence of QCD string operators

TL;DR

This paper derives explicit solutions for the scale dependence of QCD twist-2 string operators using conformal symmetry, providing a comprehensive understanding of their evolution in coordinate space.

Contribution

It presents a general solution to the evolution equations for QCD twist-2 string operators, expanding them over orthogonal eigenfunctions and explicitly detailing their leading-order scale dependence.

Findings

Explicit formulae for LO scale dependence of quark and gluon operators

Eigenfunctions determined via conformal symmetry constraints

Solution expressed as expansion over orthogonal eigenfunctions

Abstract

We have obtained a general solution of evolution equations for QCD twist-2 string operators in form of expansion over complete set of orthogonal eigenfunctions of evolution kernels in coordinate-space representation. In the leading logarithmic approximation the eigenfunctions can be determined using constraints imposed by conformal symmetry. Explicit formulae for the LO scale-dependence of quark and gluon twist-2 string operators are given.