A New Probe of Relic Neutrino Clustering using Cosmogenic Neutrinos

We propose a new probe of cosmic relic neutrinos (C$\nu$B) using their resonant scattering against cosmogenic neutrinos. Depending on the lightest neutrino mass and the energy spectrum of the cosmogenic neutrino flux, a Standard Model vector meson (such as a hadronic $\rho$) resonance can be produced via $\nu\bar{\nu}$ annihilation. This leads to a distinct absorption feature in the cosmogenic neutrino flux at an energy solely determined by the meson mass and the neutrino mass, apart from redshift. By numerical coincidence, the position of the $\rho$-resonance overlaps with the originally predicted peak of the Greisen-Zatsepin-Kuzmin (GZK) neutrino flux, which offers an enhanced absorption effect at higher redshifts. We show that this absorption feature in the GZK neutrino flux may be observable in future radio-based neutrino observatories, such as IceCube-Gen2 radio, provided there exists a large overdensity in the C$\nu$B distribution. This therefore provides a new probe of C$\nu$B clustering at large redshifts, complementary to the laboratory probes (such as KATRIN) at zero redshift.