Muon Energy Spectrum from the Analysis of Inclined Shower Footprint

Pedro Afonso De Brito Tomé

Key information

Authors:

Pedro Afonso De Brito Tomé (Pedro Afonso De Brito Tomé)

Supervisors:

Bernardo António Neto Gomes Baptista Tomé (Bernardo António Neto Gomes Baptista Tomé); Ruben Maurício da Silva Conceição (Ruben Maurício da Silva Conceição)

Published in

June 25, 2025

Abstract

Ultra high energy cosmic rays strike the atmosphere and create extensive air showers at energies unattainable by the Large Hadron Collider. The number of muons detected at ground level is a key observable for determining the primary mass composition. Long-term measurements, show that existing hadronic interaction models predict fewer muons than are observed—a discrepancy known as the Muon Puzzle. Moreover, the muon energy spectrum is not consistent across different models at high energies. In this work, we make use of the deflection caused by the Earth's magnetic field to assess the muon energy spectrum. After determining the geomagnetic field configuration producing the highest separation between positive and negative muons coming from 80 degree showers, we introduce a variable named Muon Azimuthal Distribution, which characterizes the shape of the muon footprint on the ground. The study focuses on 10 GeV, 100 GeV, and 1 TeV muons, analyzing how their final spatial distribution is affected by the physical and geometrical mechanisms involved in the shower development. To understand the contribution of each effect, we performed simulations incorporating the impact of individual mechanisms — Coulomb and multiple scattering, decay processes, and the combined set of electromagnetic processes. We then extended the analysis by considering different production altitudes, examining how the resulting azimuthal distributions evolved. Finally, using the muon energy spectrum to assign appropriate weights to the distributions corresponding to each energy, we obtained a representative distribution for the spectrum considered. This offered new clues toward resolving the muon energy spectrum at high energies.