Neutron Electric Dipole Moment on the Lattice: a Theoretical Reappraisal

TL;DR

This paper proposes a lattice-based method to evaluate the neutron electric dipole moment induced by the strong CP violation in QCD, utilizing axial Ward identities to simplify the calculation.

Contribution

It introduces a new lattice evaluation strategy for the neutron EDM that replaces the topological charge operator with flavor-singlet pseudoscalar density using Ward identities.

Findings

The method involves only disconnected diagrams.

It applies to lattice formulations with explicit chiral symmetry breaking.

The approach simplifies the calculation of the neutron EDM on the lattice.

Abstract

We present a strategy for a lattice evaluation of the neutron electric dipole moment induced by the strong CP violating term of the QCD Lagrangian. Our strategy is based on the standard definition of the electric dipole moment, involving the charge density operator J0, in case of three flavors with non-degenerate masses. We present a complete diagrammatic analysis showing how the axial chiral Ward identities can be used to replace the opological charge operator with the flavor-singlet pseudoscalar density PS. Our final result is characterized only by disconnected diagrams, where the disconnected part can be either the single insertion of PS or the separate insertions of both PS and J0. The applicability of our strategy to the case of lattice formulations that explicitly break chiral symmetry, like the Wilson and Clover actions, is discussed.