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

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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 nu 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 hadronic consequent UHECR spectra. This imprint keeps memory both of the primary UHE nu spectra as well as of the possible relic neutrino masses values, energy spectra and relic densities. Such an hadronic showering imprint should reflect into spectra morphology of cosmic rays near and above GZK 10¹⁹-10²¹eV cut-off energies. A possible neutrino degenerate masses at eVs or a more complex and significant neutrino mass split below or near Super-Kamiokande mνSK= 0.1 eV masses might be reflected after each corresponding Z peak showering, into new twin unexpected UHECR flux modulation behind GZK energies: Eₚ sim 3(fractriangle mνSK/mν10²¹),eV. Other shadowsof lightest, nearly massless, neutrinos mnu₂ₖ simeq 0.001eV simeq kTν, their lowest relic temperatures, energies and densities might be also reflected at even higher energies edges near Grand Unification: Eₚ 2.2(mν₂ₖ/ₑν)10²³, eV.