Cosmic Ray Spectrum and Tachyonic Neutrino

Abstract

In the cosmic ray spectrum, there are two knees (abrupt changes of slopes) located around the energies $E_{th}=10^{15.5}$ eV and $10^{17.8}$ eV respectively. Based on the pioneering work by Kostelecky and Ehrlich, we ascribe the first knee to a sudden opening of the reaction channel $\tildeν_e+p\to n+e^+$ when the proton has a velocity just exceeding a critical value and so can absorb a tachyonic neutrino $ν_e$ in the form of an antineutrino $\tildeν_e$. Similarly, the second knee is triggered by the reaction $\tildeν_μ+p\to Λ+μ^+$. The fitting of these two values of $E_{th}$ gives the tachyon mass of $ν_e$ and $ν_μ$ being 0.54 eV/$c^2$ and 0.48 eV/$c^2$ 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.