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We prove that twist-3 soft-gluon-pole (SGP) cross section for single spinasymmetries is determined by a certain ``primordial'' twist-2 cross section upto kinematic and color factors in the leading order perturbative QCD. Thisunveils universal structure behind the SGP cross sections in a variety of hardprocesses, and also the special role of the scale invariance in thecorresponding primordial cross section, which leads to remarkablesimplification of the SGP cross sections for the production of masslessparticle, such as those for pion production p^\uparrow p \to \pi X anddirect-photon production p^\uparrow p \to \gamma X.

Novel Master Formula for Twist-3 Soft-Gluon-Pole Mechanism to Single Transverse-Spin Asymmetry