$CP$-odd gluonic operators in QCD spin physics

Abstract

We explore connections between high energy QCD spin physics and $CP$-odd scalar gluonic operators ${\tilde{F}}^{\mu \nu }{F}_{\mu \nu }$ and ${\tilde{F}}_{\mu \nu }{F}^{\mu \alpha }{F}_{\alpha }^{\nu }$, 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.

Comments: 12 pages. v2: trivial numerical mistakes in Eqs(71,72) corrected, references added