Weinberg operator contribution to the nucleon electric dipole moment in the quark model

Abstract

We evaluate the contribution of the CP violating gluon chromo-electric dipole moment (the so-called Weinberg operator, denoted as w) to the electric dipole moment (EDM) of nucleons in the nonrelativistic quark model. The CP-odd interquark potential is modeled by the perturbative one-loop level gluon exchange generated by the Weinberg operator with massive quarks and gluons. The nucleon EDM is obtained by solving the nonrelativistic Schroedinger equation of the three-quark system using the Gaussian expansion method. It is found that the resulting nucleon EDM, which may reasonably be considered as the short-distance effect, is smaller than the long distance one obtained after "γ 5 -rotating" the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules. We estimate the total contribution to be d n = w × 20 e MeV and d p = −w × 18 e MeV with 60% of theoretical uncertainty.

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

“…Finally, let us derive an explicit constraint on the magnitude of the Weinberg operator from the presently available experimental data, given by the EDM of 199 Hg. According to our analysis, the EDM of 199 Hg is d Hg = w (µ = 1GeV) (−1.3 ± 0.96) × 10 −2 e MeV where the central value is given only by the contribution of the intrinsic neutron EDM and the error is obtained by the taking the quadrature of the theoretical uncertainty of the Weinberg operator contribution of the neutron EDM (60%) [98], the error associated with the nuclear level calculation (30%) [139], and the maximal value of the our Weinberg operator result (the second term of (5-18)), which we consider here to be a systematic error. Combined with the experimental result, d Hg (exp) < 7.4 × 10 −30 e cm [15], this leads to…”

“…[60]. The second term stands for the irreducible term calculated in the quark model (d (irr) n ≈ −5 w e MeV) [98]. We explicitly see from the above equation that the nucleon EDM generated by w has no chiral suppression.…”

“…is known to be unobservably small [91][92][93]. While the effect of the Weinberg operator to the nucleon EDM has already been evaluated [66,[94][95][96][97][98][99][100], its contribution to the CP-odd nuclear force, which is expected to be one of the leading effects to the atomic and nuclear EDMs, is less known.…”

Electric dipole moments from colour-octet scalars

“…(2.2) at the hadronic scale to the electric dipole moments of the neutron d n , proton d p and mercury d Hg are computed with non-perturbative techniques of strong interactions at low energies. State-of-the art coefficients for the CEDMs and Weinberg operator have been obtained in the literature with QCD sum rules [46][47][48][49] and the quark model [50], while the contribution of the quark EDMs can be computed in lattice QCD [51][52][53][54][55], these having significantly smaller errors. Assuming a Peccei-Quinn mechanism, these read [56]…”

Nucleon matrix element of Weinberg's CP-odd gluon operator from the instanton vacuum

“…Lattice QCD calculations are limited by the fact that higher-dimensional operators mix with lower-dimensional ones of the same quantum numbers with power-divergent coefficients, requiring accurate nonperturbative treatment of the operator mixing [9]. Estimates using effective models of hadron structure such as the quark model [10] are uncertain because these models usually do not specify how the effective degrees of freedom match with the non-perturbative gluon fields of QCD. Methods based on QCD vacuum structure, such as the estimate of Ref.…”