Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Twist-3 Formalism for Single Transverse Spin Asymmetry Reexamined: Semi-Inclusive Deep Inelastic Scattering

Hisato Eguchi, Yuji Koike, Kazuhiro Tanaka

TL;DR

The paper revisits the twist-3 mechanism for single-spin asymmetries in semi-inclusive DIS, rederiving a complete cross-section within collinear factorization that includes hard-pole, soft-fermion-pole, and soft-gluon-pole contributions from quark-gluon correlations. It shows that Ward identities impose stringent constraints on the partonic hard parts, enabling a gauge-invariant, non-overlapping factorization formula expressed in terms of the complete twist-3 distribution set (F-type and D-type). A systematic collinear expansion is developed to guarantee gauge invariance and simplify calculations, with explicit demonstration that all pole contributions satisfy the consistency relations. The paper also provides a practical SSA estimate using a soft-gluon-pole model and analyzes the relative size of derivative and non-derivative SGP terms, highlighting their phenomenological relevance for SIDIS.

Abstract

We study the single spin asymmetry (SSA) for the pion production in semi-inclusive deep inelastic scattering, $ep^\uparrow\to eπX$, in the framework of the collinear factorization. We derive the complete cross section formula associated with the twist-3 quark-gluon correlation functions for the transversely polarized nucleon, including all types of pole (hard-pole, soft-fermion-pole and soft-gluon-pole) contributions which produce the strong interaction phase necessary for SSA. We prove that the partonic hard part from each pole contribution satisfies certain constraints from Ward identities for color gauge invariance. We demonstrate that the use of these new constraints is crucial to reorganize the collinear expansion of the Feynman diagrams into manifestly gauge-invariant form so as to obtain the factorization formula for the cross section in terms of a complete set of the twist-3 distributions without any double counting. It also provides a simpler method for the actual calculation. We also present a simple estimate of SSA based on our cross section formula, using a model for the ``soft-gluon-pole function'' that represents the relevant twist-3 quark-gluon correlation, and compare the magnitude of the terms involving the derivative of the soft-gluon-pole function with that of the ``non-derivative'' terms.

Twist-3 Formalism for Single Transverse Spin Asymmetry Reexamined: Semi-Inclusive Deep Inelastic Scattering

TL;DR

The paper revisits the twist-3 mechanism for single-spin asymmetries in semi-inclusive DIS, rederiving a complete cross-section within collinear factorization that includes hard-pole, soft-fermion-pole, and soft-gluon-pole contributions from quark-gluon correlations. It shows that Ward identities impose stringent constraints on the partonic hard parts, enabling a gauge-invariant, non-overlapping factorization formula expressed in terms of the complete twist-3 distribution set (F-type and D-type). A systematic collinear expansion is developed to guarantee gauge invariance and simplify calculations, with explicit demonstration that all pole contributions satisfy the consistency relations. The paper also provides a practical SSA estimate using a soft-gluon-pole model and analyzes the relative size of derivative and non-derivative SGP terms, highlighting their phenomenological relevance for SIDIS.

Abstract

We study the single spin asymmetry (SSA) for the pion production in semi-inclusive deep inelastic scattering, , in the framework of the collinear factorization. We derive the complete cross section formula associated with the twist-3 quark-gluon correlation functions for the transversely polarized nucleon, including all types of pole (hard-pole, soft-fermion-pole and soft-gluon-pole) contributions which produce the strong interaction phase necessary for SSA. We prove that the partonic hard part from each pole contribution satisfies certain constraints from Ward identities for color gauge invariance. We demonstrate that the use of these new constraints is crucial to reorganize the collinear expansion of the Feynman diagrams into manifestly gauge-invariant form so as to obtain the factorization formula for the cross section in terms of a complete set of the twist-3 distributions without any double counting. It also provides a simpler method for the actual calculation. We also present a simple estimate of SSA based on our cross section formula, using a model for the ``soft-gluon-pole function'' that represents the relevant twist-3 quark-gluon correlation, and compare the magnitude of the terms involving the derivative of the soft-gluon-pole function with that of the ``non-derivative'' terms.

Paper Structure

This paper contains 8 sections, 51 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Formalism for the Twsit-3 mechanism in QCD
  3. A complete set of Twist-3 distribution functions
  4. Kinematics for $ep^\uparrow\to e\pi X$
  5. Collinear expansion and gauge invariance
  6. Pole contribution to the cross section
  7. Unpolarized cross section
  8. Calculation of the single-spin-dependent cross section

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 :