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.