# One-loop renormalization of staple-shaped operators in continuum and lattice regularizations

Constantinou, Martha (Department of Physics, Temple University, Philadelphia, Pennsylvania 19122—1801, USA) ; Panagopoulos, Haralambos (Department of Physics, University of Cyprus, POB 20537, 1678 Nicosia, Cyprus) ; Spanoudes, Gregoris (Department of Physics, University of Cyprus, POB 20537, 1678 Nicosia, Cyprus)

15 April 2019

Abstract: In this paper we present one-loop results for the renormalization of nonlocal quark bilinear operators, containing a staple-shaped Wilson line, in both continuum and lattice regularizations. The continuum calculations were performed in dimensional regularization, and the lattice calculations for the Wilson/clover fermion action and for a variety of Symanzik-improved gauge actions. We extract the strength of the one-loop linear and logarithmic divergences (including cusp divergences), which appear in such nonlocal operators; we identify the mixing pairs which occur among some of these operators on the lattice, and we calculate the corresponding mixing coefficients. We also provide the appropriate ${\mathrm{RI}}^{\prime }$-like scheme, which disentangles this mixing nonperturbatively from lattice simulation data, as well as the one-loop expressions of the conversion factors, which turn the lattice data to the $\overline{\mathrm{MS}}$ scheme. Our results can be immediately used for improving recent nonperturbative investigations of transverse momentum-dependent distribution functions on the lattice. Finally, extending our perturbative study to general Wilson-line lattice operators with $n$ cusps, we present results for their renormalization factors, including identification of mixing and determination of the corresponding mixing coefficients, based on our results for the staple operators.

Published in: Physical Review D 99 (2019)
Published by: APS
DOI: 10.1103/PhysRevD.99.074508
License: CC-BY-4.0