  We study the transverse momentum dependent (TMD) parton distributions in the
newly proposed quasi-parton distribution function framework in Euclidean space.
A soft factor subtraction is found to be essential to make the TMDs calculable
on lattice. We show that the quasi-TMDs with the associated soft factor
subtraction can be applied in hard QCD scattering processes such as Drell-Yan
lepton pair production in hadronic collisions. This allows future lattice
calculations to provide information on the non-perturbative inputs and energy
evolutions for the TMDs. Extension to the generalized parton distributions and
quantum phase space Wigner distributions will lead to a complete nucleon
tomography on lattice.
