Prime–index parametrization for total neutrino-nucleon cross sections and 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 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 parametrization first proposed by Heisenberg.