Constraints on Neutrino Secret Interactions from Multi-messenger Neutrinos Scattering on C$ν$B

Abstract: We present new constraints on neutrino secret interactions ($\nu$SI) by studying high-energy neutrinos from well-known astrophysical sources, such as SN1987A, the blazars TXS $0506+056$ and PKS $0735+178$, the active galaxy NGC 1068, and KM3-230213A neutrino event. We extend existing limits by covering a previously unconstrained region of the mediator mass parameter space. Our analysis focuses on Dirac neutrinos interacting with a massive spin-one boson as they propagate through the Cosmic Neutrino Background. We consider both ultra-relativistic and non-relativistic regimes, deriving bounds on the $\nu$SI coupling constant across the full $\nu$SI mediator mass range. Our results obtained using analytical methods, demonstrate significant constraints on the $\nu$SI coupling in the low-mass mediator mass region for a given cutoff parameter.