Gluon nonlocal operator mixing in lattice QCD

In this study, we explore the renormalization of a comprehensive set of gauge-invariant gluon nonlocal operators on the lattice. We calculate the renormalization factors for these operators in the modified Minimal Subtraction $(\overline{\mathrm{M}\mathrm{S}})$ scheme up to one-loop, using both dimensional and lattice regularizations in the Wilson gluon action. To facilitate a non-perturbative renormalization approach, we examine an appropriate version of the modified regularization-invariant (${\mathrm{R}\mathrm{I}}^{\mathrm{\prime }}$) scheme and determine the conversion factors from this scheme to $\overline{\mathrm{M}\mathrm{S}}$. As an integral part of this procedure, by employing symmetry arguments on the lattice, we identify the mixing pattern of these operators under renormalization.