Prime-Index Parametrization for Total Neutrino-Nucleon Cross Sections and {\it{pp}} Cross Sections

TL;DR

This paper introduces a prime number-based parametrization method for neutrino-nucleon and proton-proton cross sections, effectively modeling data across a wide energy spectrum including recent IceCube measurements.

Contribution

It presents a novel prime-index approach to accurately reproduce neutrino and proton-proton cross sections over many energy decades, linking prime number theory with high-energy particle physics.

Findings

Accurately models neutrino-nucleon cross sections from MeV to PeV energies.

Provides estimates consistent with IceCube astrophysical neutrino data.

Explains the (s) parametrization for high-energy pp cross sections.

Abstract

A prime number based parametrization for total neutrino-nucleon cross section is presented. The method employs the relation between prime numbers and their indices to reproduce neutrino cross sections for neutrino energies from the $MeV$ to the $PeV$ regions where experimental data are available. This prime-index relation provides estimates of the neutrino-nucleon cross sections valid across many decades of neutrino energy scales. The $PeV$ data are from the recently published astrophysical $\nu_\mu + \bar \nu_\mu$ rates in the IceCube detector as well as neutrino-nucleon cross section measurements. A similar method has been employed for high energy $pp$ cross sections which explains the $(\ln s)^{2}$ parametrization first proposed by Heisenberg.