Computing mean logarithmic mass from muon counts in air shower experiments

Abstract

I discuss the conversion of muon counts in air showers, which are observable by experiments, into mean logarithmic mass, an important variable to express the mass composition of cosmic rays. Stochastic fluctuations in the shower development and statistical fluctuations from muon sampling can subtly bias the conversion. A central theme is that the mean of the logarithm of the muon number is not identical to the logarithm of the mean. It is discussed how that affects the conversion in practice. Simple analytical formulas to quantify and correct such biases are presented, which are applicable to any kind of experiment.

References in corpus (1)

• A likelihood method to cross-calibrate air-shower detectors

Cited by in corpus (8)

• The Muon Puzzle in cosmic-ray induced air showers and its connection to the Large Hadron Collider
• Report on Tests and Measurements of Hadronic Interaction Properties with Air Showers
• Ultra-High-Energy Cosmic Rays: The Intersection of the Cosmic and Energy Frontiers
• Measurements of All-Particle Energy Spectrum and Mean Logarithmic Mass of Cosmic Rays from 0.3 to 30 PeV with LHAASO-KM2A
• Core-corona effect in hadron collisions and muon production in air showers
• Probing the energy spectrum of hadrons in proton air interactions at ultrahigh energies through the fluctuations of the muon content of extensive air showers
• Muon deficit in air shower simulations estimated from AGASA muon measurements
• Potential for measuring the longitudinal and lateral profile of muons in TeV air showers with IACTs