Ultra-high-energy cosmic rays are measured indirectly through the extensive air showers they trigger in the atmosphere, whose two key observables are the depth of shower maximum (Xmax) and the number of muons reaching the ground (Nmu). The 'muon puzzle' is the persistent, statistically significant excess of measured muons over the predictions of every hadronic interaction model tuned to accelerator data, indicating an incomplete description of soft, forward, and high-energy-scale hadron production. Because air showers probe center-of-mass energies and forward phase space beyond the reach of the LHC, while colliders constrain the same hadronic physics in controlled conditions, the two fields impose mutual constraints on each other: accelerator measurements calibrate the models used to interpret cosmic-ray data, and the air-shower muon deficit points to hadronic effects such as a reduced neutral-pion energy fraction in the Heitler-Matthews cascade that new collider and observatory measurements are needed to resolve.
Measurements of the products of UHECR interactions with the Earth's atmosphere, as obtained in Extended Air Shower experiments, offer important information concerning hadronic interactions, which for…