Constraining the strangeness enhancement scenario of the UHECR muon puzzle with LHC experiments

Abstract

The excess of muons observed in ultra-high-energy cosmic-ray air showers relative to simulation predictions, known as the muon puzzle, provides indirect evidence of our incomplete understanding of high-energy hadronic interactions. An unambiguous resolution requires that each proposed solution be directly tested through cosmic-ray and collider experiments probing hadronic interactions. 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, which can connect a model prediction and cosmic-ray and collider measurements. Using the \textsc{MCEq} air-shower simulation package, we first identify the key phase-space regions of hadronic interactions that drive muon yields in this scenario. Subsequent analysis demonstrates that a strangeness enhancement starting at $10^6-10^7~\mathrm{GeV}$ can consistently explain the latest cosmic-ray experiments and requires substantial enhancement at the Large Hadron Collider (LHC) energy. Furthermore, evaluating the required precision for LHC measurements, assuming Pierre Auger Observatory muon measurements and forthcoming kaon-to-pion ratio data from LHC Run~3, reveals that these experiments can robustly constrain the majority of the scenario's parameters. In particular, achieving 10.8\% precision on the kaon-to-pion ratio at LHCb and 8.4\% at FASER is sufficient to test the strangeness enhancement scenario over its viable parameter space. These upcoming experimental results will provide the first direct constraints on strangeness enhancement as a potential resolution of the muon puzzle.

Figures (7)

• Figure 1: Contour plots showing regions enclosing 50% (dotted), 75% (dashed), and 95% (solid) of the total effect for a $10^{10}$ GeV proton primary. The left panel displays the combined response over all projectile types; the right and lower-left panels show the contributions from proton, neutron, and $\pi^+$ projectiles, respectively. The coverage of experiments is shown in the bottom right panel. The pseudorapidity acceptance of the collider experiment is shown in the hatched regions, assuming $p_T$ from 0.1 to 1.0 $\mathrm{GeV}$ for $\eta=5.0$ and $p_T$ from 0.1 to 0.5 $\mathrm{GeV}$ for $\eta=8.0$.
• Figure 2: Contours enclosing 50% (dotted), 75% (dashed), and 95% (solid) of the total effect for a $10^8$ GeV proton primary. The left panel displays the combined response over all projectile types; the right and lower-left panels show the contributions from proton, neutron, and $\pi^+$ projectiles, respectively. The coverage of experiments is shown in the bottom right panel. The pseudorapidity acceptance of the collider experiment is shown in the hatched regions, assuming $p_T$ from 0.1 to 1.0 $\mathrm{GeV}$ for $\eta=5.0$ and $p_T$ from 0.1 to 0.5 $\mathrm{GeV}$ for $\eta=8.0$.
• Figure 3: Allowed region in the $(\kappa, E_{\text{start}})$ plane, where the parameters $\kappa$ and $E_{\text{start}}$ are defined in Eq. \ref{['eq:swap_basic']}, that reproduces the PAO muon count. The solid line corresponds to the PAO central value (for $x_{\text{lab}}^{\text{thr}} = 10^{-12}$, effectively no threshold). The grey-hatched band indicates the $\pm 1\sigma$ range. Dash-dotted, dash–double-dotted, and dotted lines mark where $\zeta$ reaches 1.0, 0.5, and 0.3, respectively, at $10^{10}$ GeV.
• Figure 4: The ratio of the number of muons with respect to the original prediction by SIBYLL 2.3d. The parameter sets reproducing the central PAO value are applied to emulate the strangeness enhancement. The horizontal axis shows $\log_{10}(E_{\rm start}/\mathrm{GeV})$ value from the parameter sets that reproduce the central value of the PAO measurement. The ratio is calculated for five different primary cosmic-ray energies, $10^{7}$ (solid line), $10^{8}$ (dotted line), $10^{8.5}$ (dashed line), $10^{9.5}$ (dash-dotted line) and $10^{10}~\mathrm{GeV}$ (dash-two-dotted line). The composition fractions from the Auger experiment AugerComposition2017 are used for $10^{8.5}$, $10^{9.5}$, and $10^{10}~\mathrm{GeV}$, while the composition fractions by the GSF 2025 Dembinski:2025nmp are used for $10^{7}$ and $10^{8}~\mathrm{GeV}$
• Figure 5: Expected constraint from a projected LHCb Run 3 measurement (hatched region) assuming no observed enhancement at 2.5% precision ($\zeta_{\text{LHCb}} = 0.00 \pm 0.025$), calculated for $E_{\text{start}} = 10^{6}$ GeV. The black dashed and dotted lines are the PAO central value (dashed) and $\pm 1\sigma$ range (dotted) of the Auger muon measurement (same as in Fig. \ref{['fig:param_space']}). Magenta dash-dotted and dash–double-dotted lines indicate $\zeta = 1.0$ and $0.5$ at $10^{10}$ GeV, respectively.