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 RI'-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 MS-bar scheme. Our results can be immediately used for improving recent nonperturbative investigations of transverse momentum-dependent distribution functions (TMDs) 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.
Highlights
One of the main research directions of nuclear and particle physics is the study of the rich internal structure of hadrons, which are the building blocks of the visible Universe
We have studied the one-loop renormalization of the nonlocal staple-shaped Wilson-line quark operators, both in dimensional regularization (DR) and on the lattice (Wilson/clover massless fermions and Symanzikimproved gluons)
This is a follow-up calculation of Ref. [33], in which straight-line nonlocal operators are studied
Summary
One of the main research directions of nuclear and particle physics is the study of the rich internal structure of hadrons, which are the building blocks of the visible Universe. Quantum chromodynamics (QCD) is the theory governing the strong interactions, which are responsible for binding partons (quark and gluons) together into hadrons. Despite the various theoretical models that have been developed for the investigation of hadron structure (e.g., diquark spectator and chiral quark models), an ab initio calculation is desirable to capture the full QCD dynamics. Due to the complexity of the QCD Lagrangian, an analytic solution is not possible, and numerical simulations (lattice QCD) may be used as a first principle formulation to study the properties of fundamental particles
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