LAUSR

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 (${\mathrm{RI}}^{\ensuremath{'}}$)-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 ${\mathrm{RI}}^{\ensuremath{'}}$ and the $\overline{\mathrm{MS}}$ schemes. From our results regarding the $\overline{\mathrm{MS}}$-renormalized Green's functions, one can easily derive conversion factors relating numerous variants of ${\mathrm{RI}}^{\ensuremath{'}}$-like schemes to $\overline{\mathrm{MS}}$. To make our results easily accessible, we also provide them in the form of a Mathematica input file and, also as Supplemental Material, an equivalent text file.