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The analytical expressions for the ultrarelativistic transverse momentumdistributions of the Tsallis and the Tsallis-$2$ statistics were obtained. Wefound that the transverse momentum distribution of the Tsallis-factorizedstatistics, which is now largely used to describe the experimental transversemomentum spectra of hadrons measured in $pp$ collisions at LHC and RHICenergies, in the ultrarelativistic case is not equivalent to the transversemomentum distributions of the Tsallis and the Tsallis-$2$ statistics. However,we revealed that this distribution exactly coincides with the transversemomentum distribution of the Tsallis-$2$ statistics in the zeroth termapproximation and is transformed to the transverse momentum distribution of theTsallis statistics in the zeroth term approximation by changing the parameter$q$ to $1/q_{c}$. We demonstrated analytically on the basis of theultrarelativistic ideal gas that the Tsallis-factorized statistics is notequivalent to the Tsallis and the Tsallis-$2$ statistics. In the present paperthe Tsallis statistics corresponds to the standard expectation values.

Ultrarelativistic transverse momentum distribution of the Tsallis statistics