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

TL;DR

This paper calculates the standard model contribution to the electric dipole moments of light nuclei and atomic systems, providing a detailed theoretical framework and numerical estimates for these CP-violating observables.

Contribution

First calculation of nuclear EDMs from standard model CP violation using meson exchange forces and renormalization group evolution.

Findings

Nuclear EDMs are of order 10^{-31} e cm.

Standard model contributions to atomic EDMs are very small.

Uncertainties are analyzed and potential improvements discussed.

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 $|\Delta S| = 1$ four-quark operators are matched to the $|\Delta S| = 1$ standard model processes involving the CP phase of the Cabibbo-Kobayashi-Maskawa matrix at the electroweak scale and run down to the hadronic scale $\mu = 1$ 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 $|\Delta S| = 1$ 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.