  We study transverse momentum dependent factorization and resummation at
sub-leading power in Drell-Yan and semi-inclusive deep inelastic scattering. In
these processes the sub-leading power contributions to the cross section enter
as a kinematic power correction to the leptonic tensor, and the kinematic,
intrinsic, and dynamic sub-leading contributions to the hadronic tensor. By
consistently treating the power counting of the interactions, we demonstrate
renormalization group consistency. We calculate the anomalous dimensions of the
kinematic and intrinsic sub-leading correlation functions at one loop and find
that the evolution equations give rise to anomalous dimension matrices which
mix leading and sub-leading power distribution functions. Additionally we
calculate the hard and soft functions associated with each of these
contributions. We find that these hard and soft contributions differ from those
at the leading power. Finally, we calculate the rapidity anomalous dimension
for the dynamic sub-leading distributions and find that it is the same as the
leading power anomalous dimension. We then comment on the implications for the
soft function associated with this contribution. Using this information, we
establish the factorization formalism at sub-leading power for these processes
at the one-loop level.
