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

TL;DR

This paper estimates the contribution of the Weinberg three-gluon operator to atomic and nuclear electric dipole moments using QCD sum rules and chiral perturbation theory, providing constraints on CP violation.

Contribution

It presents a novel calculation of the Weinberg operator's impact on EDMs and derives bounds from experimental data, advancing understanding of CP violation sources.

Findings

The $^{199}$Hg EDM is mainly from intrinsic nucleon EDM.

The $^{129}$Xe EDM may be dominated by Weinberg operator-induced nuclear force.

An upper limit on the Weinberg operator magnitude is established as |w| < 4×10^{-10} GeV^{-2}.

Abstract

The contribution of the CP violating three-gluon Weinberg operator, $\frac{1}{3!} w f^{abc} \epsilon^{\nu \rho \alpha \beta} G^a_{\mu \nu} G^b_{\alpha \beta} G^{c \mu}_{\rho}$, 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 $^{199}$Hg, $^{129}$Xe, $^{225}$Ra, $^2$H, and $^3$He are finally given including comprehensive uncertainty analysis. While the leading contribution of the $^{199}$Hg EDM is given by the intrinsic nucleon EDM, that of $^{129}$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 $^{199}$Hg atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of $\left|w \right| < 4 \times 10^{-10} {\rm GeV}^{-2}$ if we assume that it is the only source of CP violation at the scale $\mu =1$ TeV.