Muonium fine structure: theory update, tests of Lorentz violation and experimental prospects

Abstract

We review the status of the QED calculations for the muonium $2S_{1/2}-2P_{3/2}$ energy interval and provide the updated theoretical value of $9874.357\pm 0.001\mathrm{MHz}$. Additionally, we present a model for probing Lorentz-violating coefficients within the Standard Model Extension framework using the fine structure measurement in the presence and absence of a weak external magnetic field, enabling novel tests of CPT and Lorentz symmetry. Using Monte Carlo simulations, we estimate that a precision of $\sim 10\mathrm{kHz}$ on the isolated $2S_{1/2},F=1-2P_{3/2},F=1$ transition could be achievable employing Ramsey's separate oscillatory fields (SOF) technique. Collecting the required statics will become feasible with the upcoming High-Intensity Muon Beam (HiMB) at the Paul Scherrer Institute (PSI) in Switzerland. These advancements will enable precise tests of radiative QED corrections and nuclear self-energy contributions, while also providing tests of new physics and sensitivity to unconstrained coefficients for Lorentz violation within the Standard Model Extension framework.