Master formula for twist-3 soft-gluon-pole mechanism to single transverse-spin asymmetry

Yuji Koike,Kazuhiro Tanaka

doi:10.1016/j.physletb.2007.01.044

Abstract

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.

Highlights

We prove that twist-3 soft-gluon-pole (SGP) cross section for single spin asymmetries is determined by a certain “primordial” twist-2 cross section up to kinematic and color factors in the leading order perturbative QCD
We have revealed universal structure behind the twist-3 mechanism [5, 6], which we discuss here
The derivative with respect to p′ is taken under p′2 = 0, and Hjq(x′, x) denote the partonic hard-scattering functions which participate in the unpolarized twist-2 cross section for DY

Summary

Introduction

We prove that twist-3 soft-gluon-pole (SGP) cross section for single spin asymmetries is determined by a certain “primordial” twist-2 cross section up to kinematic and color factors in the leading order perturbative QCD. We have derived the master formula for the SGP cross section, which embodies the remarkable structure that the SGP contributions from many Feynman diagrams of the type of Fig. 1 are united into a derivative of the 2-to-2 partonic Born diagrams without the coherent-gluon line: The SSA for the DY process can be expressed as [5]

Results

Conclusion