On the contribution of twist-3 multi-gluon correlation functions to single transverse-spin asymmetry in SIDIS

TL;DR

This paper investigates how twist-3 three-gluon correlation functions inside a transversely polarized nucleon contribute to the single transverse-spin asymmetry in D-meson production during semi-inclusive deep inelastic scattering, providing a gauge-invariant factorization formula.

Contribution

It defines the complete set of twist-3 three-gluon correlation functions, derives the gauge-invariant single-spin-dependent cross section, and reveals relations to twist-2 cross sections in SSA phenomena.

Findings

Derived the gauge-invariant factorization formula for SSA in SIDIS.

Identified five independent azimuthal structures in the cross section.

Demonstrated the relation between twist-3 and twist-2 cross sections.

Abstract

We study the single spin asymmetry (SSA) induced by purely gluonic correlation inside a nucleon, in particular, by the three-gluon correlation functions in the transversely polarized nucleon, $p^\uparrow$. This contribution is embodied as a twist-3 mechanism in the collinear factorization framework and controls the SSA to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), $ep^\uparrow \rightarrow eDX$. We define the relevant three-gluon correlation functions in the nucleon, and determine their complete set at the twsit-3 level taking into account symmetry constraints in QCD. We derive the single-spin-dependent cross section for the $D$-meson production in SIDIS, taking into account all the relevant contributions at the twist-3 level. The result is obtained in a manifestly gauge-invariant form as the factorization formula in terms of the three-gluon correlation functions and reveals the five independent structures with respect to the dependence on the azimuthal angle for the produced $D$ meson. We also demonstrate the remarkable relation between the twist-3 single-spin-dependent cross section and twist-2 cross sections for the $D$-meson production, as a manifestation of universal structure behind the SSA in a variety of hard processes.