  In this work, we study the renormalization of nonlocal quark bilinear
operators containing an asymmetric staple-shaped Wilson line at the one-loop
level in both lattice and continuum perturbation theory. These operators enter
the first-principle calculation of transverse momentum-dependent parton
distribution functions (TMDPDFs) in lattice QCD using the formulation of Large
Momentum Effective Theory. We provide appropriate RI$'$-type conditions that
address the power and logarithmic divergences, as well as the mixing among
staple operators of different Dirac structures, using a number of different
possible projectors. A variant of RI$'$, including calculations of rectangular
Wilson loops, which cancel the pinch-pole singularities of the staple operators
at infinite length and reduce residual power divergences, is also employed. We
calculate at one-loop order the conversion matrix, which relates the
quasi-TMDPDFs in the RI$'$-type schemes to the reference scheme $\overline{\rm
MS}$ for arbitrary values of the renormalization momentum scale and of the
dimensions of the staple.
