Neutron electric dipole moment from lattice QCD

Abstract

We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the θ term. We develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic form factor F3 at small θ, in which NEDM is given by lim q2 →0θ F3 (q2)/(2 mN), where q is the momentum transfer and mN is the nucleon mass. We first derive a formula which relates F3, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/or the current. In the expansion of θ, 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 F3. 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 2GeV on a 163x32x16 lattice. At the quark mass mfa=0.03, corresponding to mπ/mρ 0.63, we accumulate 730 configurations, which allow us to extract the parity-odd part in both two- and three-point functions. Employing two different Dirac γ matrix projections, we show that a consistent value for F3 cannot be obtained without the subtraction described above. We obtain F3 (q2 0.58 GeV2) /(2 mN)=-0.024(5)e. fm for the neutron and F3 (q2 0.58 GeV2)/(2 mN)=0.021(6)e. fm for the proton. © 2005 The American Physical Society.