2019/08/20 by A. R. Fazely, Ali R. Fazely
Mathematics · Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Cross section (physics) #Mathematics #Neutrino #Neutrino Physics Research #Neutrino oscillation #Nuclear physics #Nucleon #Parametrization (atmospheric modeling) #Particle physics #Particle physics theoretical and experimental studies #Physics #Prime (order theory) #Quantum mechanics #hep-ph
paper · pdf · doi:10.1088/1361-6471/ab3d20
9 pages, 4 figures. J. Phys. G: Nucl. Part. Phys (2019)
openalex publication_date 2019/08/20 · openalex created_date 2019/08/29 · arxiv created 2019/08/30 · arxiv updated 2019/09/02 · openalex updated_date 2026/08/05
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> </mml:msub> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>ln</mml:mi> <mml:mi>s</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> parametrization first proposed by Heisenberg.