Neutron electric dipole moment with external electric field method in lattice QCD

Abstract

We discuss a possibility that the neutron electric dipole moment (NEDM) can be calculated in lattice QCD simulations in the presence of the $CP$-violating $\ensuremath{\theta}$ term. In this paper we measure the energy difference between spin-up and spin-down states of the neutron in the presence of a uniform and static external electric field. We first test this method in quenched QCD with the renormalization group improved gauge action on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at ${a}^{\ensuremath{-}1}\ensuremath{\simeq}2\text{ }\text{ }\mathrm{GeV}$, employing two different lattice fermion formulations, the domain-wall fermion and the clover fermion for quarks, at relatively heavy quark mass $({m}_{PS}/{m}_{V}\ensuremath{\simeq}0.85)$. We obtain nonzero values of the NEDM from calculations with both fermion formulations. We next consider some systematic uncertainties of our method for the NEDM, using ${24}^{3}\ifmmode\times\else\texttimes\fi{}32$ lattice at the same lattice spacing only with the clover fermion. We finally investigate the quark mass dependence of the NEDM and observe a nonvanishing behavior of the NEDM toward the chiral limit. We interpret this behavior as a manifestation of the pathology in the quenched approximation.