Neutron electric dipole moment with external electric field method in   lattice QCD
  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 $\theta$ term. In this paper we measure the energy difference between spin-up and spin-down states of the neutron in the presence of an uniform and static external electric field. We first test this method in quenched QCD with the RG improved gauge action on a $16^3\times 32$ lattice at $a^{-1}\simeq$ 2 GeV, employing two different lattice fermion formulations, the domain-wall fermion and the clover fermion for quarks, at relatively heavy quark mass $(m_{PS}/m_V \simeq 0.85)$. We obtain non-zero values of NEDM from calculations with both fermion formulations. We next consider some systematic uncertainties of our method for NEDM, using $24^3\times 32$ lattice at the same lattice spacing only with the clover fermion. We finally investigate the quark mass dependence of NEDM and observe a non-vanishing behavior of NEDM toward the chiral limit. We interpret this behavior as a manifestation of the pathology in the quenched approximation. 
E. Shintani, S. Aoki, N. Ishizuka, K. Kanaya, Y. Kikukawa, Y.   Kuramashi, M. Okawa, A. Ukawa, T. Yoshi\'e