Gauging the cosmic ray muon puzzle with the Forward Physics Facility

We investigate the observed muon deficit in air shower simulations when compared to ultrahigh-energy cosmic ray (UHECR) data. Gleaned from the observed enhancement of strangeness production in ALICE data, the associated $\pi \leftrightarrow K$ swap is taken as a cornerstone to resolve the muon puzzle via its corresponding impact on the shower evolution. We develop a phenomenological model in terms of the $\pi \leftrightarrow K$ swapping probability $F_s$. We provide a parametrization of $F_s (E^{\rm (proj)}, \eta)$ that can accommodate the UHECR data, where $E^{\rm (proj)}$ is the projectile energy and $\eta$ the pseudorapidity. We also explore a future game plan for model improvement using the colossal amount of data to be collected by LHC neutrino detectors at the Forward Physics Facility (FPF). We calculate the corresponding sensitivity to $F_s$ and show that the FPF experiments will be able to probe the model phase space.