The GZK cutoff smeared

The observed energy spectrum of ultra high energy cosmic rays (UHECR) is distorted by errors in the energy reconstruction. We estimate the UHECR spectrum at the Earth assuming it is originated from a cosmological flux. We then convolute this flux assuming a lognormal error in the energy. We show that if the standard deviation of the lognormal error distribution is equal or larger than 0.25, not only the shape but also the normalization of the measured energy spectra will be modified. As a consequence the GZK cutoff might be sufficiently smeared and as not to be seen. 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 is needed but also that the shape of the energy error distribution has to be known well