  Quark bilinear operators with staple-shaped Wilson lines are used to study
transverse-momentum-dependent parton distribution functions (TMDPDFs) from
lattice quantum chromodynamics (QCD). Here, the renormalization factors for the
isovector operators, including all mixings between operators with different
Dirac structures, are computed nonperturbatively in the
regularization-independent momentum subtraction scheme for the first time. This
study is undertaken in quenched QCD with three different lattice spacings. With
Wilson flow applied to the gauge fields in the calculations, the operator
mixing pattern due to chiral symmetry breaking with the lattice regularization
is found to be significantly different from that predicted by one-loop lattice
perturbation theory calculations. These results constitute a critical step
towards the systematic extraction of TMDPDFs from lattice QCD.
