StrongCPviolation and the neutron electric dipole moment reexamined

The relation between the $\mathrm{CP}$-violating operator $\theta F\tilde{F}$ and its effective version $L_{\mathrm{CP}}^{\mathrm{eff}}$ is reconsidered on the basis of the anomalous Ward-Takahashi (WT) identity. The consistency of the previous phenomenological calculations of the neutron electric dipole moment (NEDM) with the WT identity is critically examined. We demonstrate a consistent evaluation of the $O\left(N_c^0\right)$ contribution to the NEDM and the result is compared with the leading term in the chiral expansion which is $O\left(N_c^{-1\mathrm{}}\right)$.