Universal Structure of Twist-3 Soft-Gluon-Pole Cross Sections for Single Transverse-Spin Asymmetry

Abstract

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 $p^\uparrow p\to πX$ and direct-photon production $p^\uparrow p\to γX$.

Figures (2)

• Figure 1: Generic Feynman diagram contributing to twist-2 unpolarized cross section for $p p\to \pi X$, through the "$q(xp)+q(x'p')\to q(P_h/z)+q(xp+x'p'-P_h/z)$" scattering channel. White circles denote the hard scattering between partons.
• Figure 2: Generic Feynman diagrams contributing to SGP mechanism for SSA, through interference between the scatterings, $qqg \rightarrow qq$ and $qq \rightarrow qq$. Mirror diagrams also contribute.