Standard model contribution to the electric dipole moment of the deuteron, 3H, and 3He nuclei

Abstract

We calculate for the first time the electric dipole moment (EDM) of the deuteron, 3 H, and 3 He nuclei generated by the one-meson exchange CP-odd nuclear force in the standard model. The effective |∆S| = 1 four-quark operators are matched to the |∆S| = 1 standard model processes involving the CP phase of the Cabibbo-KobayashiMaskawa 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 |∆S| = 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 6 Li, 9 Be nuclei, and the atomic EDMs of 129 Xe, 199 Hg, 211 Rn, and 225 Ra generated through the nuclear Schiff moment. We then analyze the source of theoretical uncertainties and show some possible ways to overcome them.

Electric dipole moments of atoms, molecules, nuclei, and particles

“…For both the electron and the neutron, the SM CKM contribution lies several orders of magnitude below the sensitivities of recent and next-generation EDM searches. The Penguin process generated by the exchange of a kaon between two nucleons induces CP-violating effects in nuclei; however Donoghue et al (1987) and Yamanaka and Hiyama (2016) show that this contribution is also many orders of magnitude below current experimental sensitivity for diamagnetic atom EDMs. EDMs of the neutron and atoms also uniquely constrain the SM strong-interaction parameterθ which sets the scale of strong CP violation as discussed in Sec.…”

Electric dipole moment of C13

“…We should not forget to show the standard model contribution generated by the CP phase of the CabibboKobayashi-Maskawa matrix [41]:…”

“…The first advantage is the absence of electrons which screen the EDM of the nucleus, as dictated by the theorem of Schiff [34]. The second one is the small contribution from the standard model CP violation [35], which makes it an experimentally clean observable [36][37][38][39][40][41]. The final reason is the potential enhancement of the EDM by the nuclear many-body effect [42][43][44].…”

Enhancements and suppressions of CP-violating effect in the nucleons, nuclei, and atoms

“…At the hadron level, this is possible through two distinct |∆S| = 1 interactions, with one generated by the tree level W boson exchange diagram, and the other induced by the penguin diagram. We also point that the latter contribution is enhanced by the renormalization group evolution by more than an order of magnitude [69,146]. With these hadronic inputs, the nucleon EDM generated by the CKM matrix is d N ∼ 10 −32 e cm [147].…”