Nucleon electric dipole form factor in QCD vacuum

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.