CKM benchmarks for electron electric dipole moment experiments

Abstract

All current experiments searching for an electron electric dipole moment (EDM) ${d}_{e}$ are performed with atoms and diatomic molecules. Motivated by significant recent progress in searches for an EDM-type signal in diatomic molecules with an uncompensated electron spin, we provide an estimate for the expected signal in the Standard Model due to the Cabibbo-Kobayashi-Maskawa (CKM) phase. We find that the main contribution originates from the effective electron-nucleon operator $\overline{e}i{\ensuremath{\gamma}}_{5}e\overline{N}N$, induced by a combination of weak and electromagnetic interactions at $O({G}_{F}^{2}{\ensuremath{\alpha}}^{2})$, and not by the CKM-induced electron EDM itself. When the resulting atomic $P,T$-odd mixing is interpreted as an equivalent electron EDM, this estimate leads to the benchmark ${d}_{e}^{\text{equiv}}(\text{CKM})\ensuremath{\sim}{10}^{\ensuremath{-}38}\text{ }\text{ }e\mathrm{cm}$.