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

The contribution of the CP violating three-gluon interaction, proposed by Weinberg, to the short-range 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 3He nucleus yields doirr thorn 3He ow thorn 1/4 -1.5 w e MeV. The total 3He EDM, accounting for the intrinsic nucleon EDM, the pion-exchange and the short-range CP-odd nuclear force, is dotot thorn 3He ow thorn 1/4 20 thorn 14-11 w e MeV, with the dominant effect coming from the intrinsic nucleon EDM.

Automated summary

This study evaluates the contribution of the CP-violating three-gluon interaction proposed by Weinberg to the short-range CP-odd nuclear force. The results show that this contribution is comparable to the CP-even short-range nuclear force and has a significant impact, especially in the calculation of the electric dipole moment of the 3He nucleus.