# The $g$ factor of bound electrons as a test for physics beyond the Standard Model

## TL;DR

High-precision measurements of the $g$ factor in few-electron ions can serve as sensitive tests for new physics beyond the Standard Model, especially for hypothetical fifth forces, by analyzing isotope shifts and differences.

## Contribution

This work calculates the impact of a hypothetical fifth force on the $g$ factor and proposes using isotope shift measurements to set new bounds on such physics beyond the Standard Model.

## Key findings

- Isotope shift measurements can improve bounds on new physics by over an order of magnitude.
- Combining data from multiple isotopes enhances sensitivity to beyond Standard Model effects.
- Current experimental accuracy can constrain new physics more tightly than existing atomic data.

## Abstract

The use of high-precision measurements of the $g$ factor of few-electron ions and its isotope shifts is put forward as a probe for physics beyond the Standard Model. The contribution of a hypothetical fifth fundamental force to the $g$ factor is calculated for the ground state of H-like, Li-like and B-like ions, and employed to derive bounds on the parameters of that force. The weighted difference and especially the isotope shift of $g$ factors are used in order to increase the experimental sensitivity to the new physics contribution. It is found that, combining measurements from four different isotopes of H-like, Li-like and B-like calcium ions at currently accessible accuracy levels, experimental results compatible with King planarity would constrain the new physics coupling constant more than one order of magnitude further than the best current atomic data.