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

Abstract

Abstract The contribution of the CP violating three-gluon Weinberg operator, $$ \frac{1}{3!}w{f}^{abc}{\epsilon}^{\nu \rho \alpha \beta}{G}_{\mu \nu}^a{G}_{\alpha \beta}^b{G}_{\rho}^{c\mu} $$ 1 3 ! w f abc ϵ νραβ G μν a G αβ b G ρ cμ , 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 199Hg, 129Xe, and 225Ra atoms, as well as those of 2H and 3He nuclei are finally given including comprehensive uncertainty analysis. While the leading contribution of the 199Hg EDM is given by the intrinsic nucleon EDM, that of 129Xe atom may be dominated by the one-pion exchange CP-odd nuclear force generated by the Weinberg operator. From current experimental data of the 199Hg atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of |w| < 4 × 10−10GeV−2 if we assume that it is the only source of CP violation at the scale μ = 1 TeV.