Decay of proton into Planck neutrino in the theory of gravity

Abstract

It is considered gravitational interaction within the framework of the Newton theory and the quantum field theory. It is introduced the Planck neutrino $ν_{Pl}$. Gravitational interaction of the fields $ψψ$ includes short-range interaction $ψν_{Pl}$ and long-range interaction $ν_{Pl}ν_{Pl}$. Gravitational radiation can be identified with the Planck neutrino. The theory predicts the decay of proton into Planck neutrino. It is assumed that the Planck mass built from three fundamental constants $\hbar$, $c$ and $G$ is fixed in all the inertial frames. This leads to that the lifetime of proton relative to the decay into Planck neutrino decreases with the Lorentz factor as $\sim γ^{-5}$. Such a dependence of the lifetime of proton on the Lorentz factor yields a cut-off in the EHECRs spectrum. It is shown that the first "knee" in the EHECRs spectrum $E\sim 3\times 10^{15}$ eV corresponds to the lifetime of proton equal to the lifetime of the universe, the second "knee" $E\sim 10^{17}-10^{18}$ eV corresponds to the lifetime of proton equal to the thickness of our galactic disc. The EHECRs with the energies $E>3 \times 10^{18}$ eV can be identified with the Planck neutrinos.