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

TL;DR

This paper develops a space-time element field theory linking the cosmological constant to a theoretical ultraviolet cut-off energy, which aligns with cosmic ray 'knee' observations and explains phenomena like universe stability and high-energy neutrino non-detection.

Contribution

It introduces a novel space-time element field theory with a disordered structure, connecting the cosmological constant to a cut-off energy and proposing an effective field beyond the standard model.

Findings

Theoretical ultraviolet cut-off energy matches cosmic ray 'knee' at 3 PeV.

Proposes an effective field within the Planck energy scale.

Explains universe stability and high-energy neutrino non-detection.

Abstract

We formulated a field theory in space-time elements, which are obtained by dividing the space-time continuum into arbitrary-shaped space-time elements, such as hyper-octahedra (orthoplexes), which are aligned locally periodically, without long-range order. Each field is expressed in terms of scalar expansion functions with rotationally covariant coefficients. The cosmological constant was related to the cut-off energy of the quadratic Higgs self-energy. From the literature, examinations find an experimental break in the cosmic ray energy spectrum called 'knee' at about 3 [PeV], which agrees with this theoretical ultraviolet cut-off energy. Moreover, the expansion functions are updated to plane waves using the Lorentz/Poincar\'e covariant/invariant inner product of vectors with each four-momentum within the cut-off energy. Due to the long-range disordered alignment of space-time elements, this study newly introduces an effective field, which is not in the standard model and lies within the Planck energy. Particles are then rarely excited to the energy region between the cut-off energy and the Planck energy via extremely weak interaction solely with the effective field. The theoretical ultraviolet cut-off energy is consistent with the experimental phenomena such as the stability of our Universe, inflation in the early Universe and no detection of neutrinos above PeV-order energy.