Model-independent determinations of the electron EDM and the role of diamagnetic atoms

Timo Fleig,Martin Jung

doi:10.1007/jhep07(2018)012

Abstract

We perform model-independent analyses extracting limits for the electric dipole moment of the electron and the P,T-odd scalar-pseudoscalar (S-PS) nucleon-electron coupling from the most recent measurements with atoms and molecules. The analysis using paramagnetic systems, only, is improved substantially by the inclusion of the recent measurement on HfF+ ions, but complicated by the fact that the corresponding constraints are largely aligned, owing to a general relation between the coefficients for the two contributions. Since this same relation does not hold in diamagnetic systems, it is possible to find atoms that provide essentially orthogonal constraints to those from paramagnetic ones. However, the coefficients are suppressed in closed-shell systems and enhancements of P,T-odd effects are only prevalent in the presence of hyperfine interactions. We formulate the hyperfine-induced time-reversal-symmetry breaking S-PS nucleon-electron interaction in general atoms in a mixed perturbative and variational approach, based on electronic Dirac-wavefunctions including the effects of electron correlations. The method is applied to the Hg atom, yielding the first direct calculation of the coefficient of the S-PS nucleon-electron coupling in a diamagnetic system. This results in additionally improved model-independent limits for both the electron EDM and the nucleon-electron coupling from the global fit. Finally we employ this fit to provide indirect limits for several paramagnetic systems under investigation.

Highlights

The coefficients are suppressed in closed-shell systems and enhancements of P,T-odd effects are only prevalent in the presence of hyperfine interactions
JHEP07(2018)012 the model-independent extraction of the electron EDM: in principle, paramagnetic systems can be used to obtain both coefficients, taking into account potential cancellations [15, 16]; a problem arises from the fact that all paramagnetic systems constrain a similar combination of these two contributions [15]
The calculation of the dominant contribution induced by the S-PS-ne interaction in diamagnetic systems requires the inclusion of the hyperfine interaction on top of the corresponding calculation in paramagnetic systems, since its expectation value vanishes to leading order in a closed-shell atom, due to a vanishing spin density near its nucleus [17, 18]

Summary

Theoretical framework

The calculation of the dominant contribution induced by the S-PS-ne interaction in diamagnetic systems requires the inclusion of the hyperfine interaction on top of the corresponding calculation in paramagnetic systems, since its expectation value vanishes to leading order in a closed-shell atom, due to a vanishing spin density near its nucleus [17, 18]. Since we solve eq (2.1) variationally (i.e. by diagonalization), the effect of the external electric field in ψK(0) is taken into account to all orders in perturbation theory These states are technically electronic configuration interaction (CI) vectors [19]. The terms in eq (2.12) are just the equivalent of the electron EDM contribution via magnetic hyperfine interaction to an atomic EDM, as given by Flambaum and Khriplovich in reference [20], eq (17). These third-order terms, declared important but left untreated in reference [23], are taken into account in the present approach. The higher-order contributions in E are included automatically in the present approach

S-PS-ne coefficient in atomic mercury

Phenomenological consequences

Findings

Conclusions and outlook