Left-Chiral Neutrino Secret Interactions Probed by High-Energy Neutrinos Surviving the Cosmic Neutrino Background

This work explores the potential of astrophysical neutrinos to probe neutrino secret interactions (νSI) through their propagation in the Cosmic Neutrino Background (CνB). Using representative energies and distances for SN 1987A, NGC 1068, TXS 0506+056 and PKS 0735+178, together with distance hypotheses for KM3-230213A, we derive single-event survival benchmarks for the mediator mass and coupling. We focus on scenarios that do not populate right-handed neutrino states in the early Universe and therefore avoid the strongest cosmological constraints: a massive spin-one mediator with a left-chiral coupling to Dirac neutrinos and a scalar mediator coupled to Majorana neutrinos. We also consider scalar exchange with Dirac neutrinos, a common benchmark in propagation studies, and demonstrate that on the standard relic background its resonance is helicity suppressed, with a strength controlled by the relic-neutrino mass. The analysis covers a broad range of mediator masses, including the light-mediator, resonant and heavy-mediator regions, and accounts for the effects of the relic-neutrino masses and of cosmological evolution along the propagation path. We illustrate the main features of each scenario in a common-mass approximation, with analytic expressions for the non-relativistic and ultra-relativistic relic background, and then extend the analysis to realistic non-degenerate neutrino mass spectra. Owing to its energy, the KM3-230213A event shifts the resonant sensitivity to heavier mediators, while distant-source hypotheses increase the propagation sensitivity in this mass range.