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

Abstract

The contribution of the CP violating three-gluon interaction, proposed by Weinberg, to the shortrange CP-odd nuclear force is evaluated in the nonrelativistic quark model. We first show that the naive leading contribution generated by the quark exchange process vanishes at sufficiently short distance within the resonating group method, by considering the one-loop level gluon exchange CP-odd interquark potential induced by the Weinberg operator with massive quarks and gluons. We then estimate the true leading contribution by evaluating the gluonic correction to the CP-odd interquark potential in the closure approximation. It is found that the resulting irreducible CP-odd nuclear force is comparable to that generated by the chiral rotation of the CP-even short-range nuclear force, where the CP-odd mass calculated with QCD sum rules is used as input. The explicit calculation of the electric dipole moment (EDM) of the 3 He nucleus yields d (irr)3 He (w) = −1.5 w e MeV. The total 3 He EDM, accounting for the intrinsic nucleon EDM, the pion-exchange and the shortrange CP-odd nuclear force, is d (tot)3 He (w) = 20 +14 −11 w e MeV, with the dominant effect coming from the intrinsic nucleon EDM.

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

“…The Weinberg operator does not violate the chiral symmetry, so it is expected that the neutron EDM and the contact N N interaction are the leading contribution to atomic EDMs, and the CP-odd πN interactions are next-to-leading order (NLO) in the context of the chiral perturbation theory. However, the contribution of the contact N N interaction in light nuclei is not large [13,14] while the pion exchange contribution is enhanced in heavy nuclei, so we consider only the isovector CP-odd πN interaction…”

“…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].…”