  We find a novel mechanism for generating transverse single-spin asymmetry
(SSA) in semi-inclusive deep inelastic scattering, distinct from the known ones
which involve the Sivers and Collins functions, or their collinear twist-three
counterparts. It is demonstrated that a phase needed for SSA can be produced
purely within a parton-level cross section starting at two loops. We identify
the complete set of two-loop diagrams for SSA, and discuss their gauge
invariance and collinear factorization which features the $g_T$ distribution
function. In the $k_T$ factorization framework, many more sources for SSA
exist, and contributions from all possible two-parton
transverse-momentum-dependent parton distribution functions are presented up to
two loops and twist three.
