Explaining the KM3-230213A Detection without Gamma-Ray Emission: Cosmic-Ray Dark Radiation

Recently, a high-energy neutrino event, designated KM3-230213A, was observed by the KM3NeT/ARCA detector in the Mediterranean Sea. This event is characterized by a reconstructed muon energy of approximately 120 PeV, corresponding to a median neutrino energy of roughly 220 PeV. To understand the origin, it is essential to investigate consistency with multi-messenger observations--particularly gamma-ray constraints--in various theoretical scenarios within and beyond the Standard Model. Motivated by this, we explore the possibility that the detected event does not originate from conventional neutrinos but rather from right-handed neutrinos (sterile neutrinos) mixing with active neutrinos, leading to the observed muon signal. Such cosmic-ray dark radiation may have originated either in the early Universe or through dark matter decay in the present epoch. We show that in both cases, while satisfying existing general constraints on light sterile neutrinos, the stringent multi-messenger gamma-ray limits can be significantly alleviated. A distinct prediction of this scenario is that such events can arrive from directions through Earth that would typically attenuate conventional neutrinos. A related scenario involving cosmic-ray boosted WIMP dark matter is also discussed.