Neutron electric dipole moment on the lattice

We carry out a feasibility study toward a lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the θ term using two different approaches. In the first method, we calculate the CP-odd electromagnetic form factor F3, which becomes the NEDM in the zero momentum transfer limit. At the first order in θ , we derive a formula connecting the lattice three-point function to the CP-odd electromagnetic form factor. In the second method we directly extract the NEDM from the energy difference between spin-up and spin-down neutron states in the presence of a constant electric field, without expanding a small but non-zero θ . We test both approaches numerically, employing the domain-wall quark action with the RG improved gauge action in quenched QCD at a−1 ≃ 2 GeV on a 163 × 32× 16 lattice, and further applying the second method to the clover quark action at a similar lattice spacing and nucleon mass. We obtain good signals from both approaches. In particular the second method works well with both fermion formulations.