The non-linearity between 〈lnA〉〈lnA〉 and 〈Xmax〉〈Xmax〉 induced by the acceptance of fluorescence telescopes

The measurement of the average depth of the shower maximum is the most commonly used observable for the possible inference of the primary cosmic-ray mass composition. Currently, different experimental Collaborations process and present their data not in the same way, leading to problems in the comparability and interpretation of the results. Whereas 〈Xmax〉〈Xmax〉 is expected to be proportional to 〈lnA〉〈lnA〉 in ideal conditions, we demonstrate that the finite field-of-view of fluorescence telescopes plus the attenuation in the atmosphere introduce a non-linearity into this relation, which is specific for each particular detector setup.

► Xmax is the most common observable for the inference of the mass of UHECR.
► 〈Xmax〉〈Xmax〉 is linear with 〈lnA〉〈lnA〉 in ideal conditions.
► Current experimental observations seem to disagree at the highest energies.
► The acceptance of the fluorescence telescopes modifies the Xmax distributions.
► A non-linearity between 〈lnA〉〈lnA〉 and 〈Xmax〉〈Xmax〉 might be present in a given setup.