Five loop anomalous dimension of non-singlet quark currents in the RI' scheme

TL;DR

This paper calculates five-loop anomalous dimensions of quark fields and four-loop Green's functions in QCD within the RI' scheme, aiding lattice QCD measurements and providing results for general Lie groups.

Contribution

It presents the first five-loop anomalous dimensions and four-loop Green's functions in the RI' scheme for QCD, extending previous lower-order calculations.

Findings

Five-loop anomalous dimensions of quark fields are computed.

Four-loop Green's functions with operator insertions are provided.

Results are applicable to general Lie groups.

Abstract

We construct the five loop anomalous dimensions of the basic fields in Quantum Chromodynamics in a linear covariant gauge in the modified Regularization Invariant (RI') scheme. Using these core results we also compute the four loop Green's function where the quark mass operator and vector current are separately inserted in a quark 2-point function. These are necessary for measurements of the same quantities on the lattice. The Green's functions are provided in both the modified Minimal Subtraction (MSbar) and RI' schemes. All the results are available for a general Lie group.