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

Yuji Koike, Kazuhiro Tanaka

Abstract

Perturbative QCD relates the single transverse-spin asymmetries (SSAs) for hard processes at large transverse-momentum of produced particle to partonic matrix elements that describe interference between scattering from a coherent quark-gluon pair and from a single quark, generated through twist-3 quark-gluon correlations inside a hadron. When the coherent gluon is soft at the gluonic poles, its coupling to partonic subprocess can be systematically disentangled, so that the relevant interfering amplitude can be derived entirely from the Born diagrams for the scattering from a single quark. We establish a new formula that represents the exact rules to derive the SSA due to soft-gluon poles from the knowledge of the twist-2 cross section formula for unpolarized processes. This single master formula is applicable to a range of processes like Drell-Yan and direct-photon production, and semi-inclusive deep inelastic scattering, and is also useful to manifest the gauge invariance of the results.

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

Abstract

Perturbative QCD relates the single transverse-spin asymmetries (SSAs) for hard processes at large transverse-momentum of produced particle to partonic matrix elements that describe interference between scattering from a coherent quark-gluon pair and from a single quark, generated through twist-3 quark-gluon correlations inside a hadron. When the coherent gluon is soft at the gluonic poles, its coupling to partonic subprocess can be systematically disentangled, so that the relevant interfering amplitude can be derived entirely from the Born diagrams for the scattering from a single quark. We establish a new formula that represents the exact rules to derive the SSA due to soft-gluon poles from the knowledge of the twist-2 cross section formula for unpolarized processes. This single master formula is applicable to a range of processes like Drell-Yan and direct-photon production, and semi-inclusive deep inelastic scattering, and is also useful to manifest the gauge invariance of the results.

Paper Structure

This paper contains 3 equations, 2 figures.

Figures (2)

  • Figure 1: Generic diagrams for the hadronic tensor of $ep^\uparrow\to e\pi X$, decomposed into the three blobs as nucleon matrix element (lower), pion matrix element (upper), and partonic hard scattering by the virtual photon (middle). The first two terms, (a) and (b), in the expansion by the number of partons connecting the middle and lower blobs are relevant to the twist-3 effect induced by the nucleon.
  • Figure :