A Bayesian Approach for Strong Field QED Tests with He-like Ions

TL;DR

This paper introduces a Bayesian statistical method to analyze QED effects in He-like ions, providing a probabilistic framework to assess deviations from theory and guiding future experimental precision requirements.

Contribution

It presents a Bayesian approach for evaluating deviations in atomic transition energies, resolving contradictory conclusions from previous frequentist analyses.

Findings

No significant deviations from theory are observed with current data.

Recent experiments have reduced previously suggested deviations.

Future measurements need increased accuracy to detect potential divergences.

Abstract

Detailed comparisons between theory and experiment for quantum electrodynamics (QED) effects in He-like ions have been performed in the literature to search for hints of new physics. Different frequentist statistical analyses of the existing atomic transition energy data have shown contradictory conclusions as to the presence of possible deviations from the theory predictions. We present here an approach using Bayesian statistics which allows to assign quantitative probabilities to the different deviation models from theory for He-like ions for $Z = 5$ to 92. Potential deviations beyond the standard model or higher order QED effects are modeled with $f(Z) \propto Z^k$ functions. Considering the currently available data, no significant difference between theory and experiment is found, and we show that recent experiments have reduced the possible deviations previously observed in the literature. Using past measurements and a weighted average on the different deviation models, we indicate the accuracy required for future measurements to investigated possible divergences.