The Knees-Ankles-Toe in Cosmic Rays and the Periodic Table of Elementary Particles

Abstract

This paper posits the discovery of the new elementary particles from the energy spectrum for the knees-ankles-toe of cosmic rays. The energy spectrum from 109 eV to 1020 eV appears to follow a single power law except few breaks at the knees-ankles-toe. The power index increases at the first knee and the second knee, and decreases at the ankle. Above 4 × 1019 eV, the power index increases as the “toe”. The fine structure of the cosmic ray spectrum shows that an ankle with decrease in power index is in between the first knee and the second knee, resulting in two knees, two ankles, and one toe. This paper posits that the knees-ankles-toe are explained by the very high-energy fermions and bosons in the periodic table of elementary particles that places all known leptons, quarks, gauge bosons, and the Higgs boson in the table with the calculated masses in good agreement with observed values. In the periodic table, some high-energy dimensional fermions (Fd where d= dimensional orbital number from 5 to 11) and bosons (Bd) are involved in the knees-ankles-toe. At the knees and the toe, some parts of the energies from the energy sources of cosmic rays are spent to generate Fd and Bd, resulting in the increase of power index. The ankles are the the middle points (midpoints) between the adjacent dimensional fermions and bosons. At a midpoint, the energy is too high to keep the thermally unstable high-energy dimensional particle,resulting in the decay and the decrease of power index. The calculated masses of B8, the midpoint, F9, the midpoint, and B9, are 1.7 × 1015, 2 × 1016, 2.4 × 1017, 2.8 × 1018, and 3.2 × 1019 eV, respectively, which are in good agreement with observed 3 × 1015, 2 × 1016, 3 × 1017, 3 × 1018, and 4 × 1019 eV for the first knee, the first ankle, the second knee, the second ankle, and the toe, respectively. The mass of F10 is 4.4 × 1021 eV beyond the GZK limit, so F10 and above are not observed.