Neutron electric dipole moment on the lattice: a theoretical reappraisal

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 J(0), 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 topological charge operator with the flavor-singlet pseudoscalar density P-S. Our final result is characterized only by disconnected diagrams, where the disconnected part can be either the single insertion of P-S or the separate insertions of both P-S and J(0). The applicability of our strategy to the case of lattice formulations that explicitly break chiral symmetry, like the Wilson and Clover actions, is discussed.