Two-loop renormalization and mixing of gluon and quark energy-momentum tensor operators

TL;DR

This paper calculates one- and two-loop renormalization and mixing coefficients for gluon and quark energy-momentum tensor operators in QCD, providing essential results for lattice QCD and scheme conversions.

Contribution

It presents the first comprehensive two-loop renormalization and mixing calculations for gauge-invariant energy-momentum tensor operators in QCD, including scheme conversion factors.

Findings

Calculated two-loop mixing coefficients for gluon and quark operators.

Provided conversion factors between RI'-like schemes and MSbar.

Supplied results in accessible Mathematica and text formats.

Abstract

In this paper, we present one- and two-loop results for the renormalization of the gluon and quark gauge-invariant operators which appear in the definition of the QCD energy-momentum tensor, in dimensional regularization. To this end, we consider a variety of Green's functions with different incoming momenta. We identify the set of twist-2 symmetric traceless and flavor singlet operators which mix among themselves and we calculate the corresponding mixing coefficients for the nondiagonal components. We also provide results for some appropriate regularization-independent (RI')-like schemes, which address this mixing, and we discuss their application to nonperturbative studies via lattice simulations. Finally, we extract the one- and two-loop expressions of the conversion factors between the proposed RI' and the MSbar schemes. From our results regarding the MSbar-renormalized Green's functions, one can easily derive conversion factors relating numerous variants of RI'-like schemes to MSbar. To make our results easily accessible, we also provide them as Supplemental Material, in the form of a Mathematica input file and, also, an equivalent text file.