Renormalization of nonlocal gluon operators on the lattice

Wen study the renormalization of a complete set of gauge-invariant gluon nonlocal operators in lattice perturbation theory. We determine the mixing pattern under renormalization of these operators using symmetry arguments, which extend beyond perturbation theory. Additionally, we derive the renormalization factors of the operators within the modified minimal subtraction <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">(</a:mo><a:mover accent="true"><a:mi>MS</a:mi><a:mo stretchy="true">¯</a:mo></a:mover><a:mo stretchy="false">)</a:mo></a:math> scheme up to one loop. To enable a nonperturbative renormalization procedure, we investigate a suitable version of the modified regularization-invariant (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mrow><g:mi>RI</g:mi></g:mrow><g:mo>′</g:mo></g:msup></g:math>) scheme, and we calculate the conversion factors from that scheme to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mover accent="true"><i:mi>MS</i:mi><i:mo stretchy="true">¯</i:mo></i:mover></i:math>. The computations are performed by employing both dimensional and lattice regularizations, using the Wilson gluon action. This work is relevant to nonperturbative studies of the gluon parton distribution functions (PDFs) on the lattice. Published by the American Physical Society 2024