$CP$-odd gluonic operators in QCD spin physics

TL;DR

This paper investigates the role of $CP$-odd gluonic operators in QCD spin physics, introducing a twist-four GPD related to topological operators and linking the Weinberg operator to corrections in polarized deep inelastic scattering.

Contribution

It introduces a novel twist-four GPD associated with topological operators and connects the Weinberg operator to twist-four corrections in the $g_1$ structure function.

Findings

The twist-four GPD associated with $F_{ ho heta} ilde{F}^{ ho heta}$ is introduced.

The off-forward matrix element of the Weinberg operator relates to twist-four corrections in $g_1$.

Connections between $CP$-odd operators and spin physics are established.

Abstract

We explore connections between high energy QCD spin physics and $CP$-odd scalar gluonic operators $\tilde{F}^{\mu\nu}F_{\mu\nu}$ and $\tilde{F}_{\mu\nu}F^{\mu\alpha}F^{\nu}_{\alpha}$, the latter being called the Weinberg operator in the context of the nucleons' electric dipole moment. We first introduce the twist-four generalized parton distribution (GPD) associated with the topological operator $F_{\mu\nu}\tilde{F}^{\mu\nu}$. This has interesting applications in spin physics which go beyond the standard framework in terms of twist-two and twist-three distributions. In the second part, we show that the off-forward matrix element of the Weinberg operator is proportional to a certain twist-four correction to the $g_1$ structure function in polarized deep inelastic scattering.