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We investigate the renormalization of a class of gauge-invariant nonlocalquark bilinear operators, including a finite-length Wilson-line (calledWilson-line operators). The matrix elements of these operators are involved inthe recent "quasi-distribution" approach for computing light-cone distributionsof Hadronic Physics on the lattice. We consider two classes of Wilson-lineoperators: straight-line and staple-shaped operators, which are related to theparton distribution functions (PDFs) and transverse momentum-dependentdistributions (TMDs), respectively. We present our one-loop results for theconversion factors of straight-line operators between the RI' (appropriate fornonperturbative renormalization on the lattice) and MSbar (typically used inphenomenology) renormalization schemes in the presence of nonzero quark masses.In addition, we present the first results of our preliminary work for therenormalization of staple-shaped operators both in continuum (DimensionalRegularization) and lattice (Wilson/clover fermions and Symanzik improvedgluons) regularizations. We identify the observed mixing pairs among theseoperators, which must be disentangled in the nonperturbative investigations ofheavy-quark quasi-PDFs and of light-quark quasi-TMDs.

Perturbative investigation of Wilson-line operators in Parton Physics