Fractal Structure of Hadrons: Experimental and Theoretical Signatures

Deppman, A.

doi:10.3390/universe3030062

Cited by 17 publications

(17 citation statements)

References 71 publications

(74 reference statements)

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“…The self-similarity among the partons implies that the probability that the parent parton with mass E inside a larger system with mass M is similar to the probability given in Eq. (26), so the dependence on N that appears in the exponent must be changed to a parameter α, which remains to be determined. This parameter represents to the total number of degrees of freedom of the fractal, playing the same role of the exponent 4N − 5 in the case of the ideal gas.…”

Section: Statistical Description Of the Partonic Statementioning

confidence: 99%

Fractals, nonextensive statistics, and QCD

2020

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In this work we analyse how scaling properties of Yang-Mills field theory manifest as self-similarity of truncated n-point functions by scale evolution. The presence of such structures, which actually behaves as fractals, allow for recurrent nonperturbative calculation of any vertex. Some general properties are indeed independent of the perturbative order, what simplifies the non-perturbative calculations. We show that for sufficiently high perturbative orders a statistical approach can be used, the non extensive statistics is obtained, and the Tsallis index, q, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, where q can be calculated, resulting in a good agreement with the value obtained experimentally. We discuss how this approach allows to understand some intriguing experimental findings in high energy collisions, as the behavior of multiplicity against collision energy, long-tail distributions and the fractal dimension observed in intermittency analysis. arXiv:1908.08799v1 [hep-th]

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Section: Statistical Description Of the Partonic Statementioning

confidence: 99%

Fractals, nonextensive statistics, and QCD

2020

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“…In this work, we analyze in detail a thermodynamical system recently proposed that presents a fractal structure in its thermodynamical functions, which leads to a natural description of its properties in terms of Tsallis statistics [12], and we show that such a system presents a fractal structure in its momentum space. Three important properties for systems with fractal structure are defined in [12,38] and will be used in the present work:…”

Section: Fractals and Tsallis Statisticsmentioning

confidence: 99%

Fractal Structure and Non-Extensive Statistics

Deppman

Frederico

Megías

et al. 2018

Entropy

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The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics have been discussed in detail in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non-extensive statistics have been formulated over the last several years, in particular a fractal structure in thermodynamic functions was recently proposed as a possible origin for non-extensive statistics in physical systems. In the present work, we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such a system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that provided evidence of the connections between those fluctuations and Tsallis statistics. Finally, the scale invariance of the fractal thermodynamical system is discussed in terms of the Callan–Symanzik equation.

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“…. to final state hadrons (see, for example, 118-120 ; the above results were also an inspiration for the recent idea of the thermofractal nature of interactions [121][122][123] ).…”

Section: Self-similarity In Jet Eventsmentioning

confidence: 69%

Some intriguing aspects of multiparticle production processes

Wilk

Włodarczyk

2018

Int. J. Mod. Phys. A

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Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in phase space. They therefore serve as a reference point for more involved measurements. Distributions in phase space are usually investigated using the statistical approach, very successful in general but failing in cases of small colliding systems, small multiplicities, and at the edges of the allowed phase space, in which cases the underlying dynamical effects competing with the statistical distributions take over. We discuss an alternative approach, which applies to the whole phase space without detailed knowledge of dynamics. It is based on a modification of the usual statistics by generalizing it to a superstatistical form. We stress particularly the scaling and self-similar properties of such an approach manifesting themselves as the phenomena of the log-periodic oscillations and oscillations of temperature caused by sound waves in hadronic matter. Concerning the multiplicity distributions we discuss in detail the phenomenon of the oscillatory behaviour of the modified combinants apparently observed in experimental data.

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Fractal Structure of Hadrons: Experimental and Theoretical Signatures

Cited by 17 publications

References 71 publications

Fractals, nonextensive statistics, and QCD

Fractals, nonextensive statistics, and QCD

Fractal Structure and Non-Extensive Statistics

Some intriguing aspects of multiparticle production processes

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