Muon beams towards muonium physics: progress and prospects

TL;DR

This review surveys the rapidly evolving landscape of muon beams and muonium physics, highlighting how high-intensity, highly polarized muon sources enable precision tests of QED, searches for charged-lepton flavor violation, and novel material-science probes. It synthesizes current facilities (SμS, MUSE, MuSIC, ISIS, CMMS, Muon Campus, and emerging next-generation projects) and outlines forward-looking driver concepts (ion, proton, electron, and laser-based) together with cooling and acceleration strategies, including ionization cooling and muonium-laser methods. The manuscript also surveys experimental muonium studies, from production and bound-state spectroscopy (Lamb shift, 1S-2S, hyperfine structure) to gravity measurements with muonium, and discusses complementary muon applications (μSR and MIXE) for positive and negative muons. Collectively, the work underscores the potential of next-generation muon facilities to advance fundamental physics and materials research, while identifying detector and beamline challenges associated with very high counting rates and ultra-high-quality muonium beams. The developments portend significant scientific impact across particle/nuclear physics, condensed matter, and archaeology, driven by integrated advances in beam production, cooling, detection, and data processing.

Abstract

Advances in accelerator technology have led to significant improvements in the quality of muon beams over the past decades. Investigations of the muon and muonium enable precise measurements of fundamental constants, as well as searching for new physics beyond the Standard Model. Furthermore, by utilizing muon beams with high intensity and polarization, studies of the dynamics of the muon and muonium within atom level can offer valuable insights into material science. This review presents recent progress and prospects at the frontiers of muon beams and high-precision muonium physics. It also provides an overview of novel methods and detection techniques to achieve high sensitivities in different areas, including particle physics, nuclear physics, materials science and beyond.

Figures (31)

• Figure 1: Schematic of the muonium energy levels (not to scale), illustrating the hyperfine structure (HFS), fine structure (FS), Lamb shift (LS) of $n=1, n=2$ states and related transition frequencies.
• Figure 2: Schematic of the main components in a muon beamline. The muons produced from the target are first captured and focused by the capture solenoid. The dipole magnet bends and selects muons with specific momenta. The quadrupoles tripet are used to further focus the beam and transport muons to the experimental stations.
• Figure 3: Simulated momentum spectrum of muons detected by a virtual detector near the production target. The peak at about 30 MeV is from the surface $\mu^+$s.
• Figure 4: Map of current or future muon facilities around the world, which shows their rough locations, with the operating modes highlighted in bold. Solid circles with solid lines stand for existing facilities, while open circles with dashed lines indicate facilities under construction or in the planning stage. Representative experiments conducted at these muon sources are labeled in small text, with next-generation experiments in italics.
• Figure 5: Layout of the High Intensity Proton Accelerator at PSI (reproduced from Ref. Grillenberger:2021kyv).