Single-spin asymmetries at two loops

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 gT distribution function. In the kT 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.