Renormalization of three-quark operators with up to two derivatives at three loops

TL;DR

This paper computes three-loop renormalization constants and anomalous dimensions for three-quark operators in QCD, aiding lattice and perturbative QCD analyses.

Contribution

It provides the first complete three-loop analytic results for the renormalization of three-quark operators with derivatives, including spin states.

Findings

Confirmed previous two- and three-loop results for N=0.

Calculated gauge-independent anomalous dimensions.

Provided two-loop Green's functions for lattice matching.

Abstract

We study in QCD the $\overline{\mathrm{MS}}$ renormalization of three-quark operators with up to two covariant derivatives, which are related to $N=0,1,2$ Mellin moments of baryonic light-cone distributions amplitudes. Apart from general three-quark operators, we also consider those corresponding to spin 3/2 and 1/2 states. We present in analytic form the renormalization constants and anomalous dimensions of these operators through three loops, confirming previous two- and three-loop results for $N=0$. Furthermore, we evaluate through two loops their amputated four-point Green's functions with RI${}^\prime$/MOM four-momentum assignment, which are required for the matching of lattice results with perturbative calculations. We work in linear covariant gauge and find the anomalous dimensions to be gauge independent as expected.