Fermion selective tests of new physics with the bound electron g-factor

Abstract

The use of high-precision measurements of the $g$ factor of single-electron ions is considered as a detailed probe for physics beyond the Standard Model. The contribution of the exchange of a hypothetical force-carrying scalar boson to the $g$ factor is calculated for the ground state of H-like ions and used to derive bounds on the parameters of that force. Similarly to the isotope shift, we employ the nuclide shift, i.e. the difference for elements with different proton and/or neutron numbers, in order to increase the experimental sensitivity to the new physics contribution. In particular we find, combining available measurements with current precision with different ions, that the coupling constant for the interaction between an electron and a proton can be constrained up to three orders of magnitude better than with the best current atomic data and theory.

Figures (2)

• Figure 1: First line: exemplary Feynman diagrams depicting perturbative scalar-boson corrections to the $g$ factor of the electron from self energy (\ref{['fig:g-factor SE bound irr']}), vacuum polarization (\ref{['fig:g-factor VP bound red']}) and electron-nucleon interaction (\ref{['fig:g-factor eN']}). Second line: Bosonic vertex correction to the $g$ factor due to free-electron SE (\ref{['fig:g-factor SE free']}), the diagram contributing to the first non-vanishing $Z\alpha$ order in bound electron SE (\ref{['fig:g-factor SE first approx']}) and VP (\ref{['fig:g-factor VP first approx']}). A double line represents a Coulomb-Dirac wave function or propagator, a wavy line terminated by a triangle denotes a photon from the external magnetic field, the dashed line terminated by a square denotes a scalar from the nucleons, while the dashed line alone represents the scalar propagator, a wavy line terminated with a cross denotes a Coulomb interaction with the nucleus.
• Figure 2: Exclusion lines for electron-proton attractive (left) and repulsive (right) coupling. Solid lines are based on experimental and theoretical available data, whereas dashed ones are projections.