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

Philipp Blumer; Svenja Geissmann; Arnaldo J. Vargas; Gianluca Janka; Ben Ohayon; Paolo Crivelli

doi:10.1140/epjd/s10053-025-00971-6

2024 Impact factor 1.5

Atomic, Molecular, Optical and Plasma Physics

Precision Physics of Simple Atomic Systems – 2024

Open Access

Eur. Phys. J. D (2025) 79: 24
https://doi.org/10.1140/epjd/s10053-025-00971-6

Regular Article - Atomic Physics

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

Philipp Blumer¹^a, Svenja Geissmann¹, Arnaldo J. Vargas², Gianluca Janka³, Ben Ohayon⁴ and Paolo Crivelli¹^b

¹ Institute for Particle Physics and Astrophysics, Eth Zurich, 8093, Zurich, Switzerland
² Laboratory of Theoretical Physics, Department of Physics, University of Puerto Rico, 00936, Río Piedras, Puerto Rico
³ PSI Center for Neutron and Muon Sciences CNM, 5232, Villigen PSI, Switzerland
⁴ Physics Department, Technion-Israel Institute of Technology, 3200003, Haifa, Israel

^a philipp.blumer@cern.ch
^b paolo.crivelli@cern.ch

Received: 27 December 2024
Accepted: 20 February 2025
Published online: 26 March 2025

Abstract

We review the status of the QED calculations for the muonium $2 S_{1 / 2} - 2 P_{3 / 2}$ $2S_{1/2}-2P_{3/2}$ energy interval and provide the updated theoretical value of 9874.357(1) $MHz$ ${\,{\textrm{MHz}}\,}$ . 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 $\sim 10 k$ $\sim {10\,\mathrm{\text {k}\text {Hz}}}$ on the isolated $2 S_{1 / 2}, F = 1 - 2 P_{3 / 2}, F = 1$ $2S_{1/2}, F=1 - 2P_{3/2}, F=1$ transition could be achievable employing Ramsey’s separate oscillatory fields (SOF) technique. Collecting the required statistics 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.

© The Author(s) 2025

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.