  We present the details of a new factorized approach to semi-inclusive
deep-inelastic scattering which treats QED and QCD radiation on equal footing,
and provides a systematically improvable approximation to the extraction of
transverse momentum dependent parton distributions. We demonstrate how the QED
contributions can be well approximated by collinear factorization, and
illustrate the application of the factorized approach to QED radiation in
inclusive scattering. For semi-inclusive processes, we show how radiation
effects prevent a well-defined "photon-nucleon" frame, forcing one to use a
two-step process to account for the radiation. We illustrate the utility of the
new method by explicit application to the spin-dependent Sivers and Collins
asymmetries.
