Transverse momentum fluctuation under the Tsallis distribution at high energies

Ishihara, M.

doi:10.1142/s0218301317500719

Cited by 7 publications

(5 citation statements)

References 27 publications

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“…The results obtained here have shown that a system with fractal structure, similar to the thermofractals [25], can be understood as a natural consequence of the scale invariance of gauge field theories. We give solid grounds for phenomenological approaches that have been used to describe hadron mass spectrum [30] and multiparticle production with non extensive statistics [28][29][30][31][32][33][34][35][36][37][38], which can explain the long tail distribution observed in multiparticle production. From the recurrence method used here we understand the reason why, even at small order of perturbative QCD calculation, it is possible to describe correctly the transversal momentum distributions measured at high energies by adopting Tsallis distribution [39].…”

Section: Mainmentioning

confidence: 99%

Fractal structure in Yang-Mills fields and non extensivity

Deppman,

Megias,

Menezes

2019

Preprint

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Scaling properties of Yang-Mills fields are used to show that fractal structures are expected to be present in system described by those theories. We show that the fractal structure leads to recurrence formulas that allow the determination of non perturbative effective coupling. Fractal structures also cause the emergence of non extensivity in the system, which can be described by Tsallis statistics. The entropic index present in this statistics is obtained in terms of the field theory parameters. We apply the theory for QCD, and obtain the entropic index value, which is in good agreement with values obtained from experimental data. The Haussdorf dimension is calculated in terms of the entropic index, and the result for hadronic systems is in good agreement with the fractal dimension accessed by intermittency analysis of high energy collision data. The fractal dimension allow us to calculate the behavior of the particle multiplicity with the collision energy, showing again good agreement with data.

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Section: Mainmentioning

confidence: 99%

Fractal structure in Yang-Mills fields and non extensivity

Deppman,

Megias,

Menezes

2019

Preprint

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“…Since then, the Tsallis-like single particle distributions have been used in many branches of natural [8][9][10][11][12][13][14][15][16][17] and social sciences [18][19][20], and the field of high energy collisions is no exception [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. These studies have now established that the a global observable like the hadronic transverse momentum distribution generated from the high energy collisions (of protons on protons, for example) is describable by the 'Tsallis-like' distributions up to a very high range of transverse momentum (p t ) [37].…”

Section: Introductionmentioning

confidence: 99%

Thermal Field Theory of the Tsallis statistics

Rahaman,

Bhattacharyya,

Alam

2019

Preprint

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Classical and quantum Tsallis distributions have been widely used in many branches of natural and social sciences. But, the quantum field theory of the Tsallis distributions is relatively a less explored arena. In this article, we derive the expression for the thermal two-point functions for the Tsallis statistics with the help of the corresponding statistical mechanical formulations. We show that the quantum Tsallis distributions used in the literature appear in the thermal part of the propagator much in the same way the Boltzmann-Gibbs distributions appear in the conventional thermal field theory. As an application of our findings, we calculate the thermal mass in the φ 4 scalar field theory within the realm of the Tsallis statistics.

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“…The deviation from the Boltzmann-Gibbs statistics is small at high energies, and the values of |1−q| are close to 0.1. The effects of the small deviation from a e-mail: m isihar@koriyama-kgc.ac.jp the Boltzmann-Gibbs statistics on physical quantities, such as correlation and fluctuation [22,[26][27][28][29], have been studied.…”

Section: Introductionmentioning

confidence: 99%

Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator

Ishihara

2019

Int. J. Mod. Phys. E

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We studied chiral phase transition in the linear sigma model within the Tsallis nonextensive statistics in the case of small deviation from the Boltzmann-Gibbs (BG) statistics. The statistics has two parameters: the temperature T and the entropic parameter q. The normalized q-expectation value and the physical temperature T ph were employed in this study. The normalized q-expectation value was expanded as a series of the value (1 − q), where the absolute value |1 − q| is the measure of the deviation from the BG statistics. We applied the Hartree factorization and the free particle approximation, and obtained the equations for the condensate, the sigma mass, and the pion mass. The physical temperature dependences of these quantities were obtained numerically. We found following facts. The condensate at q is smaller than that at q ′ for q > q ′ . The sigma mass at q is lighter than that at q ′ for q > q ′ at low physical temperature, and the sigma mass at q is heavier than that at q ′ for q > q ′ at high physical temperature. The pion mass at q is heavier than that at q ′ for q > q ′ . The difference between the pion masses at different values of q is small for T ph ≤ 200 MeV. That is to say, the condensate and the sigma mass are affected by the Tsallis nonextensive statistics of small |1 − q|, and the pion mass is also affected by the statistics of small |1 − q| except for T ph ≤ 200 MeV.

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Transverse momentum fluctuation under the Tsallis distribution at high energies

Cited by 7 publications

References 27 publications

Fractal structure in Yang-Mills fields and non extensivity

Fractal structure in Yang-Mills fields and non extensivity

Thermal Field Theory of the Tsallis statistics

Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator

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