Renormalization of non-singlet quark operator matrix elements for deep-inelastic scattering

TL;DR

This paper presents a new method to compute the mixing matrix for non-singlet quark operators in deep-inelastic scattering, utilizing their renormalization structure and known anomalous dimensions, achieving high-order calculations.

Contribution

Introduces a novel approach to determine the mixing matrix using renormalization structure and forward anomalous dimensions, enabling calculations up to fifth order in _s.

Findings

Calculated the mixing matrix to fifth order in _s for large n_f

Method relies solely on renormalization structure and known anomalous dimensions

Applicable within the MS scheme for non-singlet quark operators

Abstract

We introduce a new method for calculating the mixing matrix for non-singlet quark operators including total derivatives, based solely on their renormalization structure in the chiral limit. As input, the method requires the well-known forward anomalous dimensions, which determine the evolution of parton distribution functions, and a calculation of the matrix elements of operators without total derivatives. Assuming a large number of quark flavors $n_f$, we are able to calculate the mixing matrix to fifth order in the strong coupling $\alpha_s$ in the $\overline{\mbox{MS}}$-scheme.