Twist-3 Single-Spin Asymmetry for SIDIS and its Azimuthal Structure

We derive the complete twist-3 single-spin-dependent cross section for semi-inclusive DIS, $e{p}^{\uparrow }\to e\pi X$, associated with the complete set of the twist-3 quark-gluon correlation functions in the transversely polarized nucleon, extending our previous study. The cross section consists of five independent structure functions with different azimuthal dependences, consistently with the transverse-momentum-dependent (TMD) factorization approach in the low $q_T$ region. Correspondence with the inclusive DIS limit and comparison with the TMD approach are briefly discussed.