Cosmogenic Neutrinos Challenge the Cosmic Ray Proton Dip Model

TL;DR

This paper critically tests the proton dip model for ultra-high-energy cosmic rays using recent spectrum data and neutrino flux limits, finding strong evidence against the model at over 95% confidence level.

Contribution

It performs a comprehensive three-parameter scan of the proton dip model, revealing its incompatibility with current neutrino flux limits and cosmic ray observations.

Findings

Predicted neutrino flux exceeds IceCube limits for all parameters.

Model prefers a maximal energy cutoff at sources over the GZK cutoff.

Results challenge the viability of the proton dip model at >95% confidence.

Abstract

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