Muon beams towards muonium physics: progress and prospects

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 searches 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 atomic level can offer valuable insights into materials 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.

💡 Research Summary

This review article provides a comprehensive overview of the current status, recent advances, and future prospects of muon beam facilities and high‑precision muonium physics. It begins by recalling the unique properties of the muon—a second‑generation charged lepton with a mass of 105.66 MeV/c², a lifetime of 2.2 µs, and the ability to be produced with near‑100 % polarization when originating from stopped pion decay. These attributes make muons ideal probes for a broad spectrum of scientific investigations, ranging from tests of the Standard Model to material‑science applications.

Section II surveys the major operational muon sources worldwide. The Swiss Paul Scherrer Institute (PSI) hosts the world’s most intense continuous‑wave (CW) surface‑muon beam (πE5), delivering fluxes up to 10⁸ µ⁺ s⁻¹ mA⁻¹. Japan’s J‑PARC/MUSE complex provides four distinct beamlines (D, U, S, H) covering surface, decay, low‑energy (via laser ionization), and high‑efficiency transport modes. Additional facilities—RAL/ISIS (UK), TRIUMF (Canada), and the Fermilab Muon Campus (USA)—supply both positive and negative muons in pulsed or CW configurations. The review also outlines the next‑generation projects under construction or in planning, such as China’s CSNS, CiADS, HIAF, Korea’s RAON, the US SNS, and the European Spallation Source muon‑collider concept. These initiatives aim to increase proton beam power to the multi‑megawatt regime and to build dedicated high‑intensity muon production targets, thereby enabling muon fluxes an order of magnitude higher than today.

Section III focuses on emerging technologies for muon production, transport, cooling, and acceleration. Three production pathways are discussed: (i) traditional high‑energy proton/ion drivers on rotating graphite targets, (ii) electron‑driven schemes using high‑current linacs or energy‑recovery linacs, and (iii) laser‑plasma electron sources that could generate dense electron bunches for bremsstrahlung‑mediated pion production. For beam cooling, the authors review ionization cooling (using low‑Z gas absorbers and RF re‑acceleration), frictional cooling (exploiting rapid energy loss near the Bragg peak), and a novel muonium‑laser‑ionization technique that converts thermal muonium into ultra‑cold µ⁺. Prospects for muon acceleration—RF cavities, cyclotrons, and linear accelerators—are evaluated in the context of future muon‑collider and muon‑electric‑dipole‑moment experiments.

Section IV delves into the core of muonium physics. Muonium (µ⁺e⁻) is a purely leptonic hydrogen‑like atom whose energy levels can be calculated to extraordinary precision within quantum electrodynamics (QED). The review highlights four flagship experimental programs: (1) searches for muonium–antimuonium conversion, which would signal charged‑lepton‑flavor violation (CLFV) and probe new‑physics scales up to 10⁴ TeV; (2) measurement of the muonium Lamb shift, currently known at the 10 ppm level, with plans to reach sub‑ppm precision using cryogenic target cells and frequency‑comb lasers; (3) the 1S–2S two‑photon transition, where recent laser‑spectroscopy efforts have achieved a relative uncertainty of 10⁻⁹, and future upgrades (cold muon beams, high‑finesse cavities) aim for 10⁻¹¹; (4) hyperfine‑structure (HFS) studies, where microwave spectroscopy combined with muon spin rotation (µSR) has determined the muon magnetic moment to 10⁻⁸, with ongoing efforts to improve the magnetic‑field uniformity and systematic control. The section also discusses ongoing proposals to measure the gravitational acceleration of muonium, employing atom‑interferometry and free‑fall techniques that could test the equivalence principle for antimatter at the 10⁻⁴ level.

Section V reviews applications of muon beams beyond fundamental physics. The µSR technique—exploiting the precession of polarized muon spins in local magnetic fields—has become a premier tool for probing weak magnetism, superconducting vortex lattices, spin dynamics, and hydrogen‑like impurity behavior in solids. Compared with conventional NMR or EPR, µSR offers a sensitivity improvement of one to two orders of magnitude and can access depths from a few nanometers to several millimeters. The Muon‑Induced X‑ray Emission (MIXE) method, which detects characteristic X‑rays emitted after muon capture and nuclear de‑excitation, provides non‑destructive elemental analysis with detection limits down to ppm and spatial resolution better than 10 µm. Both techniques benefit from recent advances in fast scintillators, silicon‑photomultipliers, and real‑time digital data acquisition, enabling high‑throughput experiments at modern high‑intensity facilities.

The concluding section synthesizes the overarching outlook: the convergence of higher beam intensities, superior polarization control, refined timing structures, and advanced laser‑based cooling is rapidly expanding the scientific reach of muon and muonium research. The authors argue that the next decade will see muon beams transition from specialized tools to versatile platforms that can simultaneously address precision tests of the Standard Model, search for physics beyond it, and deliver unprecedented insights into condensed‑matter phenomena. International collaboration, standardized beam diagnostics, and shared data infrastructures are identified as key enablers for realizing this vision.