Abstract
We calculate for the first time the electric dipole moment (EDM) of the deuteron, 3H, and 3He nuclei generated by the one-meson exchange CP-odd nuclear force in the standard model. The effective |ΔS| = 1 four-quark operators are matched to the |ΔS| = 1 standard model processes involving the CP phase of the Cabibbo-Kobayashi-Maskawa matrix at the electroweak scale and run down to the hadronic scale μ = 1 GeV according to the renormalization group evolution in the next-to-leading logarithmic order. At the hadronic scale, the hadron matrix elements are modeled in the factorization approach. We then obtain the one-meson (pion, eta meson, and kaon) exchange CP-odd nuclear force, which is the combination of the |ΔS| = 1 meson-baryon vertices which issue from the penguin operator and the hyperon-nucleon transition. From this CP-odd nuclear force, the nuclear EDM is calculated with the realistic Argonne v18 interaction and the CP-odd nuclear force using the Gaussian expansion method. It is found that the EDMs of light nuclear systems are of order O (10−31)e cm. We also estimate the standard model contribution to other hadronic CP violating observables such as the EDMs of 6Li, 9Be nuclei, and the atomic EDMs of 129Xe, 199Hg, 211Rn, and 225Ra generated through the nuclear Schiff moment. We then analyze the source of theoretical uncertainties and show some possible ways to overcome them.
Highlights
electric dipole moment (EDM) receives contribution from the single quark EDM and from the CP violating many-body interactions
The first attempt was done in ref. [61], where the penguin diagram [64, 65] was considered in the simple factorization approach, and it was found that the pion pole significantly enhances the nuclear EDM
The effect of the kaon exchange to the nuclear EDM was evaluated for the first time, using the ab initio Gaussian expansion method
Summary
We first match the |∆S| = 1 SM processes involving the CP phase of the CKM matrix with the effective |∆S| = 1 four-quark operators at the scale of the W boson mass μ = mW =. The SM contributions to the |∆S| = 1 four-quark processes are given in figures 1 and 2. In this perturbative evaluation, the strong coupling αs must be fixed at the scale μ = mW = 80.385 GeV. The top quark mass in the MS scheme mt = 160 GeV is fixed for theories below the scale μ = mt. We obtain the following Wilson coefficients to the next-to-leading order |∆S| = 1 four-quark interaction: C1(μ = mW ). The Wilson coefficients of eq (2.8) give the initial condition for the renormalization group evolution
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