Cosmic Ray Spectrum and Tachyonic Neutrino

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In the cosmic ray spectrum, there are two knees (abrupt changes of slopes) located around the energies Eth=10¹⁵.⁵ eV and 10¹⁷.⁸ eV respectively. Based on the pioneering work by Kostelecky and Ehrlich, we ascribe the first knee to a sudden opening of the reaction channel νₑ+p→ n+e+ when the proton has a velocity just exceeding a critical value and so can absorb a tachyonic neutrino νₑ in the form of an antineutrino νₑ. Similarly, the second knee is triggered by the reaction νμ+p→ Λ+μ+. The fitting of these two values of Eth gives the tachyon mass of νₑ and νμ being 0.54 eV/c² and 0.48 eV/c² respectively, which are in favor of a minimal three-flavor model for tachyonic neutrino with one parameter δ being estimated to be δ=0.34 eV.