Master formula for the three-gluon contribution to single spin asymmetry in semi-inclusive deep inelastic scattering

We derive a master formula for the contribution of the three-gluon correlation function in the nucleon to the twist-3 single-spin-dependent cross section for semi-inclusive deep-inelastic scattering, ep(up arrow) -> eDX. This is an extension of the similar formula known for the so-called soft-gluon-pole contribution induced by the quark-gluon correlation function in a variety of processes. Our master formula reduces the relevant interfering partonic subprocess with the participation of the three gluons to the Born cross sections for the gamma*g -> c (c) over bar scattering, which reveals the new structure behind the twist-3 single spin asymmetry and simplifies the actual calculation greatly. A possible extension to higher order corrections is also discussed.