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 10 9 eV to 10 20 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 × 10 19 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 (d F where d = dimensional orbital number from 5 to 11) and bosons () d B 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 d F and d B , 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 8 B , the midpoint, 9 F , the midpoint, and 9 B , are 1.7 × 10 15 , 2 × 10 16 , 2.4 × 10 17 , 2.8 × 10 18 , and 3.2 × 10 19 eV, respectively, which are in good agreement with observed 3 × 10 15 , 2 × 10 16 , 3 × 10 17 , 3 × 10 18 , and 4 × 10 19 eV for the first knee, the first ankle, the second knee, the second ankle, and the toe, respectively. The mass of 10 F is 4.4 × 10 21 eV beyond the GZK limit, so 10 F and above are not observed.

The Three Postulates of the Theory of Everything

“…At 72.8% dark energy, the calculated values for baryonic matter and dark matter (with the 1:5 ratio) are 4.53% (=(100 -72.8)/6) and 22.7% (=4.53 × 5), respectively, in excellent agreement with observed 4.56% and 22.7%, respectively [11] [19]. The dimensional orbitals of baryonic matter provide the base for the periodic table of elementary particles to calculate accurately the masses of all elementary particles, including quarks, leptons, gauge bosons, the Higgs boson, and the kneesankles-toe in cosmic rays [2]- [4].…”

“…The posited theory of everything based on the three postulates explains: 1) cosmology [7] [9]- [11], 2) the composition (baryonic matter, dark matter, and dark energy) in the universe [9] [11] [12], 3) the periodic table of elementary particles [2]- [4] for all elementary particles (quarks, leptons, gauge bosons, the Higgs boson, and the knees-ankles-toe in cosmic rays), 4) the galaxy evolution [13] [14], 5) superconductivity [15], and 6) black hole [16] [17], 7) thermodynamics [7], and 8) quantum mechanics [6] [7]. The theoretical results are in good agreement with the observations, and the calculated values from cosmology, the composition in the universe, and the periodic table of elementary particles are in good agreement with the observed values.…”

The Accurate Mass Formulas of Leptons, Quarks, Gauge Bosons, the Higgs Boson, and Cosmic Rays

“…As a result, α w instead of α is used to calculate The calculated value for α w is 0.02771. As described in the following paragraphs and Table 3, B 8 , F 9 and B 9 in Table 2 are observed in cosmic rays as the first knee, the second knee, and the toe, respectively, where the calculated masses are in good agreement with the observed masses [6]. The calculated energy for B 11 is 1.13 × 10 19 GeV in good agreement with the Planck mass, 1.22 × 10 19 GeV for gravity.…”

“…High-energy cosmic rays which have much higher energies than the energy of particles accelerated by the Large Hadron Collider provide the study of elementary particles beyond the capacity of particle accelerators. The cosmic ray mass formula is to the energy spectrum for the knees-ankles-toe of cosmic rays [6]. The energy spectrum from 10 9 eV to 10 20 eV appears to follow a single power law except few breaks at the knees-ankles-toe [18].…”

“…For examples, the calculated masses of muon, top quark, pion, neutron, and the Higgs boson are 105.55 MeV, 175.4 GeV, 139.54 MeV, 939.43 MeV, and 126 GeV, respectively, in excellent agreements with the observed 105.65 MeV, 173.3 GeV, 139.57 MeV, 939.27 MeV, and 126 GeV, respectively. The theoretical base of the accurate mass formulas is the periodic table of elementary particles [3]- [6]. As the periodic table of elements is derived from atomic orbitals, the periodic table of elementary particles is derived from the seven principal mass dimensional orbitals and seven auxiliary mass dimensional orbitals.…”