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Vacuum polarization corrections to the $μ^{+} μ^{-}$ spectrum

Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

^*Contact author: repko@msu.edu

Phys. Rev. D 112, 013011 – Published 28 July, 2025

DOI: https://doi.org/10.1103/yqyn-v8pn

Abstract

The energy levels of the $n = 1$ and $n = 2$ bound states of the $μ^{+} μ^{-}$ atom (true muonium) are calculated starting from a previously derived potential that correctly describes positronium to order $α^{5}$ supplemented by the known $α^{6}$ contributions. All electron vacuum polarization corrections on the true muonium levels are computed to order $α^{6}$ . The second-order perturbative contributions from all of the $α^{4}$ and $α^{5}$ terms in the potential are also included. Additional order $α^{6}$ contributions from the two-photon and three-photon annihilation processes are included in the evaluation of the ground state ( $1 {{}^{3}S}_{1} - 1 {{}^{1}S}_{0}$ ) hyperfine splitting.

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Phys. Rev. D 112, 013011– Published 28 July, 2025

Vol. 112, Iss. 1 — 1 July 2025

Received 16 May 2025
Accepted 23 June 2025

DOI: https://doi.org/10.1103/yqyn-v8pn

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Vacuum polarization corrections to the $μ^{+} μ^{-}$ spectrum

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Vacuum polarization corrections to the μ+μ− spectrum

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Vacuum polarization corrections to the $μ^{+} μ^{-}$ spectrum