Ultrarelativistic transverse momentum distribution of the Tsallis statistics

The analytical expressions for the ultrarelativistic transverse momentum distributions of the Tsallis and the Tsallis-2 statistics were obtained. We found that the transverse momentum distribution of the Tsallis-factorized statistics, which is now largely used to describe the experimental transverse momentum spectra of hadrons measured in pp collisions at LHC and RHIC energies, in the ultrarelativistic case is not equivalent to the transverse momentum distributions of the Tsallis and the Tsallis-2 statistics. However, we revealed that this distribution exactly coincides with the transverse momentum distribution of the Tsallis-2 statistics in the zeroth term approximation and is transformed to the transverse momentum distribution of the Tsallis statistics in the zeroth term approximation by changing the parameter q to 1/qc. We demonstrated analytically on the basis of the ultrarelativistic ideal gas that the Tsallis-factorized statistics is not equivalent to the Tsallis and the Tsallis-2 statistics. In the present paper the Tsallis statistics corresponds to the standard expectation values.