Hadron transverse momentum distributions of the Tsallis normalized and unnormalized statistics

Abstract

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

Propagation of non-linear waves in hot, ideal, and non-extensive quark–gluon plasma

“…It is shown in Ref. [44] that the transverse momentum spectra obtained from the single particle distribution is expressed in terms of an infinite summation and the zeroth term coincides with the phenomenological classical Tsallis distribution widely used in the literature. The forms of the Tsallis quantum distributions used in literature are similar to (but not always exactly the same as) the zeroth order approximated term when one uses the factorization approximation used in Ref.…”

“…This situation may appear due non-ideal plasma effects, fluctuation etc [42,43]. Extremizing the Tsallis thermodynamic potential with respect to p i one arrives at the expression for the Tsallis probabilities and the single particle distribution [44]. It is shown in Ref.…”

On the Difference between the Radii of Gluons and Quarks

“…The corresponding Fermi-Dirac and Bose-Einstein distributions are recovered with q → 1, where q remains a free parameter in this model. There are some studies about how to apply the non-extensivity to fermions and bosons, see e.g., [34] and references therein. Parvan and Batacharya developed [34] the fermions and bosons distributions of the transverse momentum using the grand-canonical ensemble.…”

“…There are some studies about how to apply the non-extensivity to fermions and bosons, see e.g., [34] and references therein. Parvan and Batacharya developed [34] the fermions and bosons distributions of the transverse momentum using the grand-canonical ensemble. If one expands Equation ( 3) and compares it with Equation (56) (the thermodynamical distribution part) of [34], a close similarity of the present ansatz is observed with a more rigorous study.…”

“…Parvan and Batacharya developed [34] the fermions and bosons distributions of the transverse momentum using the grand-canonical ensemble. If one expands Equation ( 3) and compares it with Equation (56) (the thermodynamical distribution part) of [34], a close similarity of the present ansatz is observed with a more rigorous study. The only difference is focusing on the longitudinal momentum in the present study.…”