  We demonstrate a factorization formula for semi-inclusive deep-inelastic
scattering with hadrons in the current fragmentation region detected at low
transverse momentum. To facilitate the factorization, we introduce the
transverse-momentum dependent parton distributions and fragmentation functions
with gauge links slightly off the light-cone, and with soft-gluon radiations
subtracted. We verify the factorization to one-loop order in perturbative
quantum chromodynamics and argue that it is valid to all orders in perturbation
theory.
