Abstract
Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormalization and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS-bar scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing, $a$, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventual $O(a)$ improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths.
Highlights
Calculating parton distribution functions (PDFs) of hadrons using lattice QCD is challenging
Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD
If the path is made from a finite number of segments, each of which is a Wilson line propagating along a lattice axis, it is straightforward to accommodate the nonlocal operator in the lattice auxiliary field framework
Summary
Calculating parton distribution functions (PDFs) of hadrons using lattice QCD is challenging. [28,29], the auxiliary field approach [30,31] was used to represent the nonlocal operator as the product of two local operators in an extended theory.. [28] we defined a lattice action for the auxiliary field with n 1⁄4 Æμpointing along one of the lattice axes, 1A similar analysis for gluonic Wilson-line operators in the continuum was done in Refs.
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