GZK cutoff distortion due to the energy error distribution shape

The development of an ultra high energy air shower has an intrinsic energy fluctuation due both to the first interaction point and to the cascade development. Here we show that for a given primary energy this fluctuation has a lognormal distribution and thus observations will estimate the primary energy with a lognormal error distribution. We analyze the UHECR energy spectrum convolved with the lognormal energy error and demonstrate that the shape of the error distribution will interfere significantly with the ability to observe features in the spectrum. If the standard deviation of the lognormal error distribution is equal or larger than 0.25, both the shape and the normalization of the measured energy spectra will be modified significantly. As a consequence, the GZK cutoff might be sufficiently smeared as not to be seen (without very high statistics). This result is independent of the power law of the cosmological flux. As a conclusion we show that in order to establish the presence or not of the GZK feature, not only more data are needed but also that the shape of the energy error distribution has to be known well. The high energy tail and the sigma of the approximate lognormal distribution of the error in estimating the energy must be at the minimum set by the physics of showers.