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The origin and composition of ultra-high-energy cosmic rays (UHECRs) remain amystery. The proton dip model describes their spectral shape in the energyrange above $10^9$ GeV by pair production and photohadronic interactions withthe cosmic microwave background. The photohadronic interactions also producecosmogenic neutrinos peaking around $10^9$ GeV. We test whether this model isstill viable in light of recent UHECR spectrum measurements from the TelescopeArray experiment, and upper limits on the cosmogenic neutrino flux fromIceCube. While two-parameter fits have been already presented, we perform afull scan of the three main physical model parameters: source redshiftevolution, injected proton maximal energy, and spectral index. We findqualitatively different conclusions compared to earlier two-parameter fits inthe literature: a mild preference for a maximal energy cutoff at the sourcesinstead of the Greisen--Zatsepin--Kuzmin (GZK) cutoff, hard injection spectra,and strong source evolution. The predicted cosmogenic neutrino flux exceeds theIceCube limit for any parameter combination. As a result, the proton dip modelis challenged at more than 95\% C.L. This is strong evidence against this modelindependent of mass composition measurements.

Cosmogenic Neutrinos Challenge the Cosmic Ray Proton Dip Model