Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory

Abstract

In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the first-principle calculation of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD using the formulation of large momentum effective theory. We provide appropriate RI′-type conditions that address the power and logarithmic divergences, as well as the mixing among staple operators of different Dirac structures, using a number of different possible projectors. A variant of RI′, including calculations of rectangular Wilson loops, which cancel the pinch-pole singularities of the staple operators at infinite length and reduce residual power divergences, is also employed. We calculate at one-loop order the conversion matrix, which relates the quasi-TMDPDFs in the RI′-type schemes to the reference scheme MS¯ for arbitrary values of the renormalization momentum scale and of the dimensions of the staple. Published by the American Physical Society 2024