  We investigate the renormalization of a class of gauge-invariant nonlocal
quark bilinear operators, including a finite-length Wilson-line (called
Wilson-line operators). The matrix elements of these operators are involved in
the recent "quasi-distribution" approach for computing light-cone distributions
of Hadronic Physics on the lattice. We consider two classes of Wilson-line
operators: straight-line and staple-shaped operators, which are related to the
parton distribution functions (PDFs) and transverse momentum-dependent
distributions (TMDs), respectively. We present our one-loop results for the
conversion factors of straight-line operators between the RI' (appropriate for
nonperturbative renormalization on the lattice) and MSbar (typically used in
phenomenology) renormalization schemes in the presence of nonzero quark masses.
In addition, we present the first results of our preliminary work for the
renormalization of staple-shaped operators both in continuum (Dimensional
Regularization) and lattice (Wilson/clover fermions and Symanzik improved
gluons) regularizations. We identify the observed mixing pairs among these
operators, which must be disentangled in the nonperturbative investigations of
heavy-quark quasi-PDFs and of light-quark quasi-TMDs.
