Astrophysical Neutrino Sources as Colliders

High-energy neutrinos arise from processes at large center-of-mass energies, offering a window to test physics at comparable scales or beyond those accessible in collider experiments on Earth. Here, we present a recipe for extracting two-sided bounds on the inelastic $pp$ and $p\gamma$ cross sections from neutrino point-source data, by independently constraining every astrophysical input (cosmic-ray luminosities and target densities) through electromagnetic observations or theoretical arguments. The cross section is then the only remaining free parameter. Applying this framework to the IceCube associations with TXS~0506+056, NGC~1068, and the Galactic Plane, to a stacked population of eleven X-ray bright Seyfert galaxies, to the ultra-high-energy KM3NeT event KM3-230213A, and to projected observations of ultra-high-energy neutrinos, we obtain constraints that span center-of-mass energies from $\sqrt{s}\sim 1$ GeV to $\sim 10^{5}$ GeV, some of which are well beyond the reach of the LHC and, for the $p\gamma$ channel, beyond HERA. Several of these bounds are more stringent than unitarity limits.