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

We investigate 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 by measuring 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 test this method in quenched QCD on a $16^3\times 32$ lattice at $a^{-1}\simeq$ 2 GeV, employing two different formulations, the domain-wall fermion and the clover fermion for quarks, at relatively heavy quark mass $(m_{PS}/m_V \simeq 0.85)$, together with the RG improved gauge action. We obtain non-zero values for NEDM for both fermion formulations. We next investigate several systematics of NEDM signals on a $24^3\times 32$ lattice in quenched QCD at the same lattice spacing with the clover fermion. In particular, we study the quark mass dependence of NEDM, and observe a behavior indicating that NEDM does not vanish toward the chiral limit, which we interpret as a manifestation of the pathology in the quenched approximation