Future Muon Physics Experiments: Muon Beams and Experimental Apparatus

Muons are powerful probes of fundamental physics at the precision and intensity frontiers. We review the status and planned upgrades of muon-beam facilities worldwide, together with the experimental apparatus required across three experimental categories. Charged-lepton flavor violation (CLFV) searches test charged-lepton flavor conservation through rare muon decays, muon-to-electron conversion in nuclei, and muonium–antimuonium conversion. Precision measurements of the muon magnetic and electric dipole moments, muonium spectroscopy, and muonic-atom spectroscopy test the Standard Model and bound-state QED and determine fundamental constants and nuclear charge and magnetization distributions. Muon-scattering programs include the MUonE determination of hadronic vacuum polarization, NA64$\mu$ missing-momentum searches for invisible dark sectors, and the phased PKMu program, which investigates muonphilic dark matter, light mediators, LFV muon–electron processes, and atomic effects in resonant annihilation. We emphasize the beam intensity, timing, purity, and phase-space control, as well as beamline and detector design, background suppression, and experimental techniques needed to achieve next-generation sensitivity and precision.