Importance and required precision of the forward experiments at the LHC for testing a strangeness enhancement scenario of the muon puzzle

The muon puzzle—the excess of muons observed in ultra-high-energy cosmic-ray air showers relative to simulation predictions—highlights our incomplete understanding of high-energy hadronic interactions. To resolve this discrepancy, each proposed solution must be subjected to direct experimental tests. In this work, we develop a framework to assess the strangeness enhancement scenario, wherein an increased yield of kaons relative to pions boosts muon production. Using the MCEq air-shower simulation package, we first identify the key phase-space regions of hadronic interactions that drive muon yields in this scenario. We then demonstrate that a synergistic analysis, combining Pierre Auger Observatory muon measurements with forthcoming kaon-to-pion ratio data from LHC Run 3, can robustly constrain the scenario’s parameters. In particular, we find that achieving 10.8 % precision on the kaon-to-pion ratio at LHCb and 8.4 % at FASER is sufficient to test the strangeness enhancement hypothesis over its viable parameter space. These upcoming experimental results will provide the first direct constraints on strangeness enhancement as a solution to the muon puzzle, marking a significant step toward its resolution.