Nucleon electric dipole form factor in QCD vacuum

TL;DR

This paper derives a new relationship between nucleon electric dipole form factors and topological properties of the QCD vacuum, enabling estimates of proton and neutron EDMs induced by CP violation.

Contribution

It introduces a novel theoretical relationship linking nucleon form factors to QCD vacuum topology, facilitating EDM calculations from topological susceptibility.

Findings

Derived explicit formulas for nucleon EDMs in terms of topological susceptibility.

Results align with recent lattice QCD estimates.

Provides a new theoretical tool for studying CP violation in QCD.

Abstract

In the QCD vacuum, the nucleon form factors receive contributions from the underlying ensemble of topological pseudoparticles, which are sensitive to a finite vacuum angle $\theta$. We use this observation to derive a novel relationship between the Pauli and electric dipole form factors, for light quark flavors. This relationship allows for an explicit derivation of the proton and neutron electric dipole moments induced by a small CP violating $\theta$ angle, in terms of the vacuum topological susceptibity times pertinent magnetic moments. The results compare well with some recent lattice estimates.