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

Osamura, Naohiro*; Gubler, P. ; Yamanaka, Nodoka*

The contribution of the CP violating three-gluon Weinberg operator to the atomic and nuclear EDMs is estimated using QCD sum rules. After calculating the transition matrix element between the pion and the vacuum through the Weinberg operator, we obtain the long-range CP-odd nuclear force by determining the isovector CP-odd pion-nucleon vertex, using chiral perturbation theory at NLO. The EDMs of Hg, Xe, and Ra atoms, as well as those of H and He nuclei are finally given including comprehensive uncertainty analysis. While the leading contribution of the Hg EDM is given by the intrinsic nucleon EDM, that of Xe atom may be dominated by the one-pion exchange CP-odd nuclear force generated by the Weinberg operator. From current experimental data of the Hg atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of if we assume that it is the only source of CP violation at the scale = 1 TeV.