A muon experimental facility, known as the Muon Science Establishment (MUSE), is one of the user facilities at the Japan Proton Accelerator Research Complex, along with those for neutrons, hadrons, and neutrinos. The MUSE facility is integrated into the Materials and Life Science Facility building in which a high-energy proton beam that is shared with a neutron experiment facility delivers a variety of muon beams for research covering diverse scientific fields. In this review, we present the current status of MUSE, which is still in the process of being developed into its fully fledged form.

To test bound-state quantum electrodynamics (BSQED) in the strong-field regime, we have performed high precision x-ray spectroscopy of the $5g–4f$ and $5f–4d$ transitions (BSQED contribution of 2.4 and 5.2 eV, respectively) of muonic neon atoms in the low-pressure gas phase without bound electrons. Muonic atoms have been recently proposed as an alternative to few-electron high-$Z$ ions for BSQED tests by focusing on circular Rydberg states where nuclear contributions are negligibly small. We determined the $5g_{9/2}–4f_{7/2}$ transition energy to be $6297.08\pm 0.04(\mathrm{stat})\pm 0.13(\mathrm{syst})\mathrm{eV}$ using superconducting transition-edge sensor microcalorimeters (5.2–5.5 eV FWHM resolution), which agrees well with the most advanced BSQED theoretical prediction of 6297.26 eV.

We observed electronic $K$ x rays emitted from muonic iron atoms using superconducting transition-edge sensor microcalorimeters. The energy resolution of 5.2 eV in FWHM allowed us to observe the asymmetric broad profile of the electronic characteristic $K\alpha$ and $K\beta$ x rays together with the hypersatellite $K^h\alpha$ x rays around 6 keV. This signature reflects the time-dependent screening of the nuclear charge by the negative muon and the $L$-shell electrons, accompanied by electron side feeding. Assisted by a simulation, these data clearly reveal the electronic $K$- and $L$-shell hole production and their temporal evolution on the 10–20 fs scale during the muon cascade process.

A systematic experimental study on muon-catalyzed fusion was conducted using a series of solid deuterium and tritium mixtures. A variety of conditions were investigated, i.e., tritium concentrations from 20% to 70%, and temperatures from 5 to 16 K. With decreasing temperature, we observed an unexpected decrease in the muon cycling rate (${\lambda }_c$) and an increase in the muon loss probability ($W$). The origins of these observed changes were interpreted by the temperature-dependence in the $dt\mu$ formation process for ${\lambda }_c$ and that in the muon reactivation process after muon-to-$\alpha$ sticking for $W$.