$CP$-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.

arXiv comment12 pages. v2: trivial numerical mistakes in Eqs(71,72) corrected, references added

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Cited by in corpus (14)

• High-energy Operator Product Expansion at sub-eikonal level
• Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated
• The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics
• Weinberg operator contribution to the nucleon electric dipole moment in the quark model
• Chiral and trace anomalies in Deeply Virtual Compton Scattering
• Chiral and trace anomalies in Deeply Virtual Compton Scattering II: QCD factorization and beyond
• Nucleon electric dipole moment from polarized deep inelastic scattering
• Parton distribution function for topological charge at one loop
• Weinberg Operator Contribution to the Hadronic CP Violation
• Weinberg operator contribution to the CP-odd nuclear force in the quark model
• Contribution of the Weinberg-type Operator to atomic and nuclear electric dipole moments
• Quark model analysis of the Weinberg operator contribution to the nucleon EDM
• Nucleon matrix element of Weinberg's CP-odd gluon operator from the instanton vacuum
• One-loop structure of parton distribution for the gluon condensate and "zero modes"