Gluon nonlocal operator mixing in lattice QCD

Abstract

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 $(\overline{\mathrm{MS}})$ 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 (${\mathrm{RI}}^{\prime }$) scheme and determine the conversion factors from this scheme to $\overline{\mathrm{MS}}$. As an integral part of this procedure, by employing symmetry arguments on the lattice, we identify the mixing pattern of these operators under renormalization.

10 pages, 2 figures, 1 table, Contribution to The 41st International Symposium on Lattice Field Theory (LATTICE2024), 28 July - 3 August 2024, Liverpool, UK