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

Abstract

The contribution of the CP violating three-gluon Weinberg operator, 1 3! w f abc νραβ G a µν G b αβ G cµ ρ , 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 |w| < 4×10 −10 GeV −2 if we assume that it is the only source of CP violation at the scale µ = 1 TeV.

Weinberg operator contribution to the CP-odd nuclear force in the quark model

“…We also note that the one-pion exchange process [Fig. 2 (c)], which is a priori subleading in χEFT, was found to not be negligible for heavy atoms through QCD sum rules calculation [113]. The reducible contribution may be evaluated like the nucleon EDM, by chirally rotating the CP-even contact interaction L N N = − 1 2 C S N N N N with C S = −120.8 GeV −2 obtained from χEFT analysis [114].…”

“…( 2). For heavy nuclei, the one-pion exchange CP-odd nuclear force generated by the WO also becomes important, and it may in some cases be comparable to the nucleon EDM effect [113,170,171]. This process is also currently affected by a large uncertainty.…”

“…With the reducible short-range CP-odd nuclear force [see Fig. 2 (a)], the EDM of 3 He nucleus was estimated to be [112,113,[115][116][117][118]…”

“…We also show the result of the QCD sum rules calculation of the CP-odd pion-exchange nuclear force induced by the WO [see Fig. 2 (c)] [113]:…”

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

“…This operator was first calculated in the Higgs doublet model [7], and then, it has been found that some other models also generate it such as the supersymmetric model [8]. While the relation between this operator and the neutron EDM has been investigated widely [9,10,11], its value for the CP-odd nucleon-nucleon (N N ) interaction, which is expected to give the main contribution to the atomic EDMs, has only been evaluated quite recently [12,13].…”