Abstract
We present an overview of a proposal in relativistic proton-proton (pp) collisions emphasizing the thermal or kinetic freeze-out stage in the framework of the Tsallis distribution. In this paper we take into account the chemical potential present in the Tsallis distribution by following a two step procedure. In the first step we used the redudancy present in the variables such as the system temperature, T, volume, V, Tsallis exponent, q, chemical potential, μ, and performed all fits by effectively setting to zero the chemical potential. In the second step the value q is kept fixed at the value determined in the first step. This way the complete set of variables T,q,V and μ can be determined. The final results show a weak energy dependence in pp collisions at the centre-of-mass energy s=20 TeV to 13 TeV. The chemical potential μ at kinetic freeze-out shows an increase with beam energy. This simplifies the description of the thermal freeze-out stage in pp collisions as the values of T and of the freeze-out radius R remain constant to a good approximation over a wide range of beam energies.
Highlights
IntroductionIt has been estimated [1] that about 30,000 particles (pions, kaons, protons, antiprotons)) are produced in a central heavy ion collision at the Large Hadron Collider (LHC) at 5.02 TeV
It has been estimated [1] that about 30,000 particles) are produced in a central heavy ion collision at the Large Hadron Collider (LHC) at 5.02 TeV
In this paper we have taken into account the chemical potential present in the Tsallis distribution
Summary
It has been estimated [1] that about 30,000 particles (pions, kaons, protons, antiprotons)) are produced in a central heavy ion collision at the Large Hadron Collider (LHC) at 5.02 TeV. For the most central Pb-Pb collisions, the best description of the ALICE data on yields of particles in one unit of rapidity at mid-rapidity was obtained for a chemical freeze-out temperature given by Tch = 156.6 ± 1.7 MeV [7,8]. In this paper we review another possibility to describe the thermal freeze-out stage which has shown considerable potential especially to describe the final state in proton–proton (pp) collisions. Most of these approaches are based on variations of a distribution proposed by Tsallis about 40 years ago [12] to describe entropy by introducing an additional parameter called q. For completeness and for the convenience of the reader we have included the tables presented there and considerably improved on them, the inclusion of the NA61/SHINE [14] is new and contributes very much to the understanding of the energy dependence of the parameters, all figures are new
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