We analyze commonly used expressions for computing the nucleon electric dipole form factors (EDFF) $F_3$ and moments (EDM) on a lattice and find that they lead to spurious contributions from the Pauli form factor $F_2$ due to inadequate definition of these form factors when parity mixing of lattice nucleon fields is involved. Using chirally symmetric domain wall fermions, we calculate the proton and the neutron EDFF induced by the CP-violating quark chromo-EDM interaction using the corrected expression. In addition, we calculate the electric dipole moment of the neutron using background electric field that respects time translation invariance and boundary conditions, and find that it decidedly agrees with the new formula but not the old formula for $F_3$. Finally, we analyze some selected lattice results for the nucleon EDM and observe that after the correction is applied, they either agree with zero or are substantially reduced in magnitude, thus reconciling their difference from phenomenological estimates of the nucleon EDM.
Nucleon Electric Dipole Moment from the $θ$ Term with Lattice Chiral Fermions
在晶格间距为0.11 fm的三种不同海π介子质量的畴壁晶格上，我们从带有重叠费米子的$θ$项计算了核子电偶极矩。由于重叠费米子的手征对称性守恒，我们定义了EDM的拓扑荷和手征极限。因此，手征外推可以在非零晶格间距可靠地进行。我们使用三到四个不同的部分猝灭价介子质量为每个海介子质量，发现EDM依赖于价和海介子质量表现相反，这可以描述的部分猝灭手征微扰理论。借助于集团分解误差约化（CDER）技术，我们确定了物理π质量下的中子和质子EDM分别为$d_{n}=-0.00148\left(14\right)\left(31\right)\barθ$ e $\cdot$ fm和$d_{p}=0.0038\left(11\right)\left(8\right)\barθ$ e $\cdot$ fm.这项工作是一个明确的示范的优势，使用手征费米子的核子EDM计算和铺平道路，未来的精确研究强$CP$违反的影响。
