  We prove that twist-3 soft-gluon-pole (SGP) cross section for single spin
asymmetries (SSA) is determined by a certain ``primordial'' twist-2 cross
section up to kinematic and color factors in the leading order perturbative
QCD. In particular, for the processes in which the partonic hard scattering
occurs among massless partons, the invariance of the ``primordial'' partonic
cross section under scale transformation leads to remarkable simplification of
the SGP cross section, reproducing compact form that was recently observed for
pion production $p^\uparrow p\to \pi X$ and direct-photon production
$p^\uparrow p\to \gamma X$.
