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

The contribution of the CP violating three-gluon Weinberg operator, 1/3!wf(abc)is an element of(v rho alpha beta)G(mu v)(a)G(alpha)(beta)(b)G(rho)(c mu), 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-199, Xe-129 and Ra-225 atoms, as well as those of H-2 and He-3 nuclei are finally given including comprehensive uncertainty analysis. While the leading contribution of the Hg-199 EDM is given by the intrinsic nucleon EDM, that of Xe-129 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-199 atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of vertical bar w vertical bar < 4 x 10(-10) GeV-2 if we assume that it is the only source of CP violation at the scale mu = 1 TeV.

Automated summary

The contribution of the CP violating three-gluon Weinberg operator to atomic and nuclear EDMs is estimated using QCD sum rules. By calculating transition matrix elements and determining the isovector CP-odd pion-nucleon vertex using chiral perturbation theory, the long-range CP-odd nuclear force is obtained. The upper limit on the Weinberg operator magnitude is derived from experimental data on the Hg-199 atomic EDM if it is considered the only source of CP violation at a scale of 1 TeV.