Implications of the Pseudo-Dirac Scenario for Ultra High Energy Neutrinos from GRBs

The source of Ultra High Energy Cosmic Rays (UHECR) is still an unresolved mystery. Up until recently, sources of Gamma Ray Bursts (GRBs) had been considered as a suitable source for UHECR. Within the fireball model, the UHECR produced at GRBs should be accompanied with a neutrino flux detectable at the neutrino telescope such as IceCube. Recently, IceCube has set an upper bound on the neutrino flux accompanied by GRBs about 3.7 times below the prediction. We investigate whether this deficit can be explained by the oscillation of the active neutrinos to sterile neutrinos en route from the source to the detectors within the pseudo-Dirac scenario. We then discuss the implication of this scenario for diffuse supernova relic neutrinos.

💡 Research Summary

The paper addresses the long‑standing puzzle of the origin of ultra‑high‑energy cosmic rays (UHECRs) by revisiting gamma‑ray bursts (GRBs) as their potential sources within the standard fireball framework. In this model, protons accelerated in internal or external shocks interact with intense photon fields, producing pions that decay into neutrinos with energies in the 10⁵–10⁷ GeV range. Consequently, a sizable flux of ultra‑high‑energy (UHE) neutrinos should accompany every GRB and be detectable by cubic‑kilometer‑scale telescopes such as IceCube. However, after several years of data taking, IceCube has reported only upper limits on the GRB‑associated neutrino flux, which lie a factor of ≈3.7 below the canonical fireball predictions. This discrepancy motivates the authors to explore whether active‑to‑sterile neutrino oscillations over cosmological distances could be responsible, specifically within the pseudo‑Dirac (or “quasi‑Dirac”) neutrino scenario.

A pseudo‑Dirac neutrino consists of two nearly degenerate Majorana states, one active (νₐ) and one sterile (νₛ), whose mass splitting Δm² is extremely small (10⁻¹⁸–10⁻¹⁴ eV²). The tiny Δm² yields an oscillation phase Δ = Δm² L/(2E) that becomes appreciable only when the baseline L is of order hundreds of megaparsecs and the neutrino energy E is in the PeV–EeV range. In vacuum the transition probability is \