No abstract

Abstract. The nuclear modification factor is derived using Tsallis non-extensive statistics in relaxation time approximation. The variation of the nuclear modification factor with transverse momentum for different values of the non-extensive parameter, q, is also observed. The experimental data from RHIC and LHC are analysed in the framework of Tsallis non-extensive statistics in a relaxation time approximation. It is shown that the proposed approach explains the RAA of all particles over a wide range of transverse momentum but does not seem to describe the rise in RAA at very high transverse momenta.PACS. 25.75.-q Relativistic heavy-ion collisions -25.75.Cj Heavy-quark production in heavy-ion collisions

Abstract. We expand the Tsallis distribution in a Taylor series of powers of (q − 1), where q is the Tsallis parameter, assuming q is very close to 1. This helps in studying the degree of deviation of transverse momentum spectra and other thermodynamic quantities from a thermalized Boltzmann distribution. After checking thermodynamic consistency, we provide analytical results for the Tsallis distribution in the presence of collective flow up to the first order of (q − 1). The formulae are compared with the experimental data.

A detailed analysis is presented of the precise values of the Tsallis parameters obtained in p − p collisions for identified particles, pions, kaons and protons at the LHC at three beam energies √ s = 0.9, 2.76 and 7 TeV. Interpolated data at √ s = 5.02 TeV have also been included. It is shown that the Tsallis formula provides reasonably good fits to the p T distributions in p − p collisions at the LHC using three parameters dN/dy, T and q. However, the parameters T and q depend on the particle species and are different for pions, kaons and protons. As a consequence there is no m T scaling and also no universality of the parameters for different particle species.

The exact analytical formulas for the transverse momentum distributions of the Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics of particles with nonzero mass in the framework of the Tsallis normalized and Tsallis unnormalized (also known as Tsallis-1 and Tsallis-2) statistics have been consistently derived. The final exact results were expressed in terms of the series expansions in the integral representation. The zeroth term approximation to both quantum and classical statistics of particles has been introduced. We have revealed that the phenomenological classical Tsallis distribution (widely used in high energy physics) is equal to the distribution of the Tsallis unnormalized statistics in the zeroth term approximation, but the phenomenological quantum Tsallis distributions (introduced by definition on the basis of the generalized entropy of the ideal gas) do not correspond to the distributions of the Tsallis statistics. We have found that in the ranges of the entropic parameter relevant to the processes of high-energy physics (q < 1 for Tsallis-1 and q > 1 for Tsallis-2) the Tsallis statistics is divergent. Therefore, to obtain physical results, we have regularized the Tsallis statistics by introducing an upper cut-off in the series expansion. The exact numerical results for the Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics of particles in the Tsallis normalized and unnormalized statistics have been obtained. We observed that the exact results of the Tsallis statistics strongly enhanced the production of high-pT hadrons in comparison with the usual phenomenological Tsallis distribution function at the same values of q. The q-duality of the Tsallis normalized and unnormalized statistics for the massive particles was studied.PACS. 13.85.-t Hadron-induced high-and super-high-energy interactions -13.85.Hd Inelastic scattering: many-particle final states -24.60.-k Statistical theory and fluctuations