The Delta Resonance in the Neutrino Sky

Recent measurements of the diffuse cosmic neutrino flux by IceCube show evidence for a spectral break at an energy near $E_\nu \sim 30$ TeV. In this letter, we suggest that this feature may be due to the $\Delta$-baryon resonance in $p\gamma$ interactions. We show that the measured spectrum, including the observed break, can be naturally accommodated by a flux of protons accelerated with a spectrum $dN_p /dE_p \propto E_p^{-3.1}$ interacting with X-rays of typical energy $E_{\gamma} \sim 0.3\,{\rm keV}$. We also point out that the presence of this spectral break significantly reduces the contribution of neutrino sources to the isotropic gamma-ray background, alleviating the longstanding tension between these measurements. In the $\Delta$-resonance scenario, the gamma rays accompanying neutrino production cascade down to MeV-GeV energies and contribute at the $\sim 10\%$ level to the isotropic gamma-ray background at $\sim 3$~GeV. If our proposal is realized, it may imply that we have identified the dominant sources that produce the extragalactic cosmic rays.