The chemical composition of ultra high energy cosmic rays is still uncertain.
The latest results obtained by the Pierre Auger Observatory and the HiRes
Collaboration, concerning the measurement of the mean value and the
fluctuations of the atmospheric depth at which the showers reach the maximum
development, Xmax, are inconsistent. From comparison with air shower
simulations it can be seen that, while the Auger data may be interpreted as a
gradual transition to heavy nuclei for energies larger than ~ 2-3x10^18 eV, the
HiRes data are consistent with a composition dominated by protons. In Ref. [1]
it is suggested that a possible explanation of the observed deviation of the
mean value of Xmax from the proton expectation, observed by Auger, could
originate in a statistical bias arising from the approximated exponential shape
of the Xmax distribution, combined with the decrease of the number of events as
a function of primary energy. In this paper we consider a better description of
the Xmax distribution and show that the possible bias in the Auger data is at
least one order of magnitude smaller than the one obtained when assuming an
exponential distribution. Therefore, we conclude that the deviation of the
Auger data from the proton expectation is unlikely explained by such
statistical effect.Comment: To be published in Journal of Physics G: Nuclear and Particle Physic