Neutron electric dipole moment from lattice QCD -: art. no. 014504

We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the theta term. We develop the strategy to obtain the nucleon EDM from the CP- odd electromagnetic form factor F-3 at small theta, in which NEDM is given by lim(q2 -> 0 theta)F(3)(q(2))/(2m(N)), where q is the momentum transfer and m(N) is the nucleon mass. We first derive a formula which relates F-3, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/ or the current. In the expansion of theta, the parity-odd part of the nucleon- current- nucleon three-point function contains contributions not only from the parity-odd form factors but also from the parity-even form factors multiplied by the parity-odd part of the nucleon two- point function, and, therefore, the latter contribution must be subtracted to extract F-3. We then perform an explicit lattice calculation employing the domain- wall quark action with the renormalization group improved gauge action in quenched QCD at a(-1) similar or equal to 2 GeV on a 16(3) x 32 x 16 lattice. At the quark mass m(f)a = 0: 03, corresponding to m(pi)/m(rho) similar or equal to 0:63, we accumulate 730 configurations, which allow us to extract the parityodd part in both two- and three- point functions. Employing two different Dirac gamma matrix projections, we show that a consistent value for F-3 cannot be obtained without the subtraction described above. We obtain F-3(q(2) similar or equal to 0:58 GeV2)/(2m(N))= -0:024(5) e . fm for the neutron and F-3(q(2) similar or equal to 0: 58 GeV2)/(2mN) = 0:021(6)e . fm for the proton.