Shadows of Relic Neutrino Masses and Spectra on Highest Energy GZK Cosmic Rays

Abstract

The Ultra High Energy (UHE) neutrino scattering onto relic cosmic neutrinos in galactic and local halos offers an unique way to overcome GZK cut-off. The UHE v secondary of UHE photo-pion decays may escape the GZK cut-off and travel on cosmic distances hitting local light relic neutrinos clustered in dark halos. The Z resonant production and the competitive W ⁺ W ^-,ZZ pair production define a characteristic imprint on hadronie consequent UHECR spectra. This imprint keeps memory both of the primary UHE v spectra as well as of the possible relic neutrino masses values, energy spectra and relic densities. Such an hadronie showering imprint should reflect into spectra morphology of cosmic rays near and above GZK (10¹⁹ — 10²¹ eV) cut-off energies. A possible neutrino degenerate masses at eVs or a more complex and significant neutrino mass split below or near Super-Kamiokande $\Delta {m_{{vsk}}} \sim 0.1eV$ masses might be reflected after each corresponding Z peak showering, into new twin unexpected UHECR flux modulation behind GZK energies: ${E_P} \sim 3\left( {\frac{{\Delta {m_{{{v_{{SK}}}}}}}}{{{m_v}}}} \right){.10^{{21}}}eV$ . Other extreme shadows of lightest, nearly massless, neutrinos ${m_{{{v_{{2K}}}}}} \simeq 0.001eV \simeq k{T_v}$ their lowest relic temperatures, energies and densities might be also reflected at even higher energies edges near Grand Unification: ${E_p} \sim 2.1\left( {\frac{{{m_{{{v_{{2K}}}}}}}}{{{E_v}}}} \right){.10^{{23}}}eV$ .