Abstract
We considered the ultrarelativistic transverse momentum distributions of the Tsallis-1 and Tsallis-2 statistics using two regularization schemes. It was revealed that the cut-off parameter strongly influences the behavior of the transverse momentum distribution in both statistics. We have also found that the ultrarelativistic transverse momentum distribution of the Tsallis-1 statistics is transformed to the momentum distribution of the Tsallis-2 statistics by identifying q → 1/ q c .
Highlights
The transverse momentum distributions of the Tsallis-factorized statistics [1, 2] are largely used to analyze the LHC and RHIC data on the transverse momentum distributions of hadrons created in the proton-proton and heavy-ion collisions
In [7] it was found out that the parameter q, which indicates the deviation of the Tsallis distribution from the usual Boltzmann distribution, effectively takes into account the hard processes of the partons reactions, which lead to the creation of energetically highpT hadrons
The analytical formulae for the ultrarelativistic transverse momentum distributions of the Tsallis-1 and Tsallis-2 statistics were derived in detail
Summary
The transverse momentum distributions of the Tsallis-factorized statistics [1, 2] are largely used to analyze the LHC and RHIC data on the transverse momentum distributions of hadrons created in the proton-proton and heavy-ion collisions. The partition function (20) for the Maxwell-Boltzmann ultrarelativistic ideal gas in the framework of the Tsallis-1 statistics in the grand canonical ensemble can be written as [6]. The mean occupation numbers for the Maxwell-Boltzmann ultrarelativistic ideal gas in the Tsallis statistics in the grand canonical ensemble for qc > 1 can be written as [6]. In the Model B, the cut-off parameter N0 is found from the inflection point of the function ln φ(N) substituting (24) into (18) The results of these two methods are illustrated in figure 2. In the Tsallis-2 statistics the transverse momentum distribution of the Model A differs essentially from the transverse momentum distribution of the Model B and the Tsallis-factorized statistics due to the large values of the cut-off parameter N0. The results of the Model B are close to the results of the Tsallis-factorized statistics, because the values of N0 in the Model B are close to zero
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