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.
Highlights
An important open question in Hadronic Physics is the hadron spin decomposition, i.e., the distribution of hadron spin among its constituent particles
In order to address the effects of gauge-variant operators, we propose an extension of the above approaches, including a semi-nonperturbative determination of the gaugevariant operators’ contributions to the renormalization factors: The gluonic and fermionic parts of the gaugevariant operators can be calculated by lattice simulations, while the ghost part and/or the gauge-fixing terms can be obtained by lattice perturbation theory
We study the two-loop renormalization and mixing of the gluon and quark energy-momentum tensor (EMT) operators in dimensional regularization
Summary
An important open question in Hadronic Physics is the hadron spin decomposition, i.e., the distribution of hadron spin among its constituent particles It is well known, by recent experiments, that contributions to the hadron spin arise from valence quarks, and from polarized gluons, as well as sea quarks. Useful quantities which give important input to the study of hadron spin structure are the quark and gluon average momentum fractions [1]. Their nonperturbative determination in nucleons is currently under investigation by a number of research groups [2–4], and so far, the outcomes are very promising for the correct extraction of the nucleon spin decomposition. There are still many challenges that need to be faced, including the complete renormalization of these quantities
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