Contribution of the Weinberg-type operator to atomic electric dipole moments

Abstract: We report the calculation of the isovector CP-odd $\pi N$ interaction generated by the Weinberg operator, the CP violating three-gluon operator. This enables to restrict models which induce the operator by using experimental data of atomic electric dipole moment. The QCD sum rules are used to determine the matrix element required to assess the CP-odd $\pi N$ interactions. The relation between the Weinberg operator and the Hg and Xe EDMs is clarified, and the constraint on the Weinberg operator is obtained using the experimental data for the Hg EDM.