Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosmic Ray Spectrum and Tachyonic Neutrino   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
$\tilde{\nu}_e+p\to n+e^+$ when the proton has a velocity just exceeding a
critical value and so can absorb a tachyonic neutrino $\nu_e$ in the form of an
antineutrino $\tilde{\nu}_e$. Similarly, the second knee is triggered by the
reaction $\tilde{\nu}_\mu+p\to \Lambda+\mu^+$. The fitting of these two values
of $E_{th}$ gives the tachyon mass of $\nu_e$ and $\nu_\mu$ 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 $\delta$ being estimated to be
$\delta=0.34$ eV.

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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an