We present a calculation of the contribution of the Θ -term to the neutron and proton electric dipole moments using seven 2 + 1 + 1 -flavor highly improved staggered quark ensembles. We also estimate the topological susceptibility for the 2 + 1 + 1 theory to be χ Q = ( 66 ( 9 ) ( 4 ) ? ? MeV ) 4 in the continuum limit at M π = 135 ? ? MeV . The calculation of the nucleon three-point function is done using Wilson-clover valence quarks. The CP form factor F 3 is calculated by expanding in small Θ . We show that lattice artifacts introduce a term proportional to a that does not vanish in the chiral limit, and we include this in our chiral-continuum fits. A chiral perturbation theory analysis shows that the N ( 0 ) π ( 0 ) state should provide the leading excited-state contribution, and we study the effect of such a state. Detailed analysis of the contributions to the neutron and proton electric dipole moment using two strategies for removing excited-state contamination are presented. Using the excited-state spectrum from fits to the two-point function, we find d n Θ is small, | d n Θ | ? 0.01 Θ ˉ ? ? e · fm , whereas for the proton we get | d p Θ | ～ 0.02 Θ ˉ ? ? e · fm . On the other hand, if the dominant excited-state contribution is from the N π state, then | d n Θ | could be as large as 0.05 Θ ˉ ? ? e · fm and | d p Θ | ～ 0.07 Θ ˉ ? ? e · fm . Our overall conclusion is that present lattice QCD calculations do not provide a reliable estimate of the contribution of the Θ -term to the nucleon electric dipole moments, and a factor of 10 higher statistics data are needed to get better control over the systematics and possibly a 3 σ result.
展开▼
