Three loop renormalization of 3-quark operators in QCD

TL;DR

This paper calculates the three-loop anomalous dimension of the proton's 3-quark operator in QCD, addressing gamma^5 issues and providing results useful for lattice QCD measurements.

Contribution

It extends the three-loop renormalization of 3-quark operators in QCD, including gamma^5 treatment and finite parts for lattice applications.

Findings

Computed three-loop anomalous dimensions for proton operators.

Extended gamma^5 treatment within dimensional regularization.

Provided finite Green's function parts for lattice QCD.

Abstract

We compute the three loop MSbar anomalous dimension for the 3-quark operator corresponding to the proton. This requires the treatment of gamma^5 within dimensional regularization as well as evanescent operators generated through the renormalization. We extend the Larin scheme for gamma^5 to a mixing matrix of finite renormalization constants chosen so that chiral symmetry is manifest in four dimensions. We also provide the finite part of the Green's function at two loops where the operator is inserted at zero momentum in a quark 3-point function in an arbitrary linear covariant gauge in order to assist with the lattice measurement of the same quantity. The renormalization of the generalized 3-quark operators in the scheme devised by Kraenkl and Manashov is extended to three loops and the anomalous dimensions for the (1/2,0), (3/2,0) and (1,1/2) spin operators with various chiralities are also given.