Why do air showers contain more muons than simulations predict?
In plain words
Cosmic rays hitting the atmosphere make cascades of particles, and measured cascades carry tens of percent more muons (heavier cousins of the electron) than computer models of particle collisions predict, which spoils estimates of what the cosmic rays are made of.
Precise statement
Auger (2016) found the muon number in showers near $1e19\,\mathrm{eV}$ larger than simulations with LHC-tuned hadronic models (EPOS-LHC, QGSJetII-04) by factors of about 1.3 to 1.6, and a combined analysis of several experiments finds a deficit in simulations that grows with energy above $\sim 1e16\,\mathrm{eV}$. Identify the missing physics in hadronic interaction models (enhanced strangeness or baryon production, reduced neutral-pion fraction, forward-region effects) consistent with collider data. Answer: a modified model reproducing muon number, $X_{\mathrm{max}}$ and muon production depth at once, with the resulting shift in inferred composition.
What would settle it
Forward-region measurements of pion and kaon production in proton-oxygen collisions at the LHC used in air-shower simulations that match measured muon numbers without breaking $X_{\max}$.