Superstatistical cluster decay

• Tsallis distributions are widely recognized.
• There are papers suggesting that some results which look like Tsallis distribution numerically are not exactly of this type.
• It is shown that they correspond to specific cases of superstatistics, which do not result in Tsallis distributions.

We provide an overview of Tsallis statistics, presented as a special case of superstatistics and applied to the multiparticle processes described by the statistical cluster model. This model combines Boltzman statistics applied to hadronization of clusters and superstatistics induced by fluctuations of their Lorentz factors. It results in a Tsallis-like distribution of transverse momenta with some scale, the origin of which is discussed. We show that this distribution becomes a Tsallis distribution in a special case, namely when one combines fluctuations of the Lorentz factor and temperature inside the cluster, given by beta and gamma distributions, respectively.