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

TL;DR

This paper evaluates the contribution of the Weinberg operator to the CP-odd nuclear force using a nonrelativistic quark model, finding it comparable to chiral rotation effects and calculating its impact on the $^3$He electric dipole moment.

Contribution

It provides a detailed estimation of the Weinberg operator's contribution to CP-odd nuclear forces within a quark model, including gluonic corrections and their effects on nuclear EDMs.

Findings

The leading contribution vanishes at short distances due to quark exchange.

Gluonic corrections yield a significant CP-odd nuclear force.

The $^3$He EDM is dominated by intrinsic nucleon EDM, with the Weinberg operator's effect quantified.

Abstract

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 $^3$He nucleus yields $d_{^3{\rm He}}^{\rm (irr)} (w) = - 1.5 \, w\, e $ MeV. The total $^3$He EDM, accounting for the intrinsic nucleon EDM, the pion-exchange and the short-range CP-odd nuclear force, is $d_{^3{\rm He}}^{\rm (tot)} (w) = 20_{-11}^{+14} \, w\, e $ MeV, with the dominant effect coming from the intrinsic nucleon EDM.