Weinberg operator contribution to the nucleon electric dipole moment in the quark model

We evaluate the contribution of the CP violating gluon chromo-electric dipole moment (the so-called Weinberg operator, denoted as $w$) to the electric dipole moment (EDM) of nucleons in the nonrelativistic quark model. The CP-odd interquark potential is modeled by the perturbative one-loop level gluon exchange generated by the Weinberg operator with massive quarks and gluons. The nucleon EDM is obtained by solving the nonrelativistic Schr\"{o}dinger equation of the three-quark system using the Gaussian expansion method. It is found that the resulting nucleon EDM, which may reasonably be considered as the irreducible contribution, is smaller than the one obtained after $\gamma_5$-rotating the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules. We estimate the total contribution to be $d_n = w \times 20 \, e \, {\rm MeV}$ and $d_p = - w \times 18 \, e \, {\rm MeV}$ with 60% of theoretical uncertainty.