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 Schr\"{o}dinger 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 irreducible contribution, is smaller than the one obtained after $\gamma_5$-rotating the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules. We estimate the total contribution to be $d_n = w \times 20 \, e \, {\rm MeV}$ and $d_p = - w \times 18 \, e \, {\rm MeV}$ with 60% of theoretical uncertainty.
Highlights
The discovery of the Higgs boson in LHC experiments [1,2] completed the particle listing of the standard model (SM), but it is known that still several cosmologically important phenomena cannot be explained
We evaluate the contribution of the CP-violating gluon chromo-electric dipole moment to the electric dipole moment (EDM) of nucleons in the nonrelativistic quark model
It is found that the resulting nucleon EDM, which may reasonably be considered as the irreducible contribution, is smaller than the one obtained after “γ5 rotating” the anomalous magnetic moment using the CP-odd mass calculated with QCD sum rules
Summary
The discovery of the Higgs boson in LHC experiments [1,2] completed the particle listing of the standard model (SM), but it is known that still several cosmologically important phenomena cannot be explained. In this work we propose to calculate the Weinberg operator contribution to the nucleon EDM in the quark model. We will evaluate the nucleon EDM generated by the Weinberg operator in the quark model with the expectation to obtain results that go beyond the accuracy of the naïve dimensional analysis (2). This will permit us to give an accurate constraint on the Weinberg operator from neutron EDM experiments. We derive the one-loop level CP-odd gluon exchange potential between quarks generated by the Weinberg operator.
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