Consideration on the relationship of theoretical ultraviolet cut-off energy with experimental data

Abstract

We formulated a field theory by using localized basis functions in space-time elements, which are obtained by dividing the space-time continuum into irregular hyper-octahedra (orthoplexes). Each field is expressed as a linear combination of the scalar basis functions (whose derivatives can be expressed in terms of the Dirac delta function) with rotationally invariant coefficients. Using this formalism mapped to continuum theory with its corresponding ultraviolet cut-off energy, the cosmological constant was related to the cut-off energy of the quadratic Higgs self-energy. Using current particle-cosmological particle and cosmological data, this study determines the Minkowski cut-off energy. From the literature, examinations find an experimental break in the cosmic ray energy spectrum called a 'knee' at about 3 PeV, which agrees with this theoretical ultraviolet cut-off energy. The origin of cosmic rays is understood astrophysically below 1 PeV, while it is unclear above 3 PeV. By analogy to solid state physics, additional energy contributions from basis functions may result in the tail of the energy spectrum above the cut-off energy. The basis functions reproduce experimental spectra above the ultraviolet cut-off energy. The knee is caused by the diffuse scattering of cosmic rays by the irregular space-time lattice. Since this diffuse scattering indicates high scattering probabilities for particles with a tiny/zero rest mass, this theory is consistent with the absence of any experimental detection of photons and neutrinos above about the knee energy.Comment: v1: 7 pages; v2: Sec. 3 and related parts revised; v3: Secs. 1 and 3 and related parts revised; v4: Secs. 3 and 4 and related parts revised; v5: a few improvements made to Abstract and related parts in Secs. 1, 3 and 4; v6: Sec. 3 and related parts modified; v7: some changes in wording and English language editing performe