Generalized Poisson distributions for systems with two-particle interactions

Hameeda, Mir; Plastino, A.; Rocca, M. C.

doi:10.1088/2633-1357/abec9f

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…) ˆ, which is consistent with the definition in equation (12). It is easy to check that 2 z á ñ ˆis also consistently defined in a similar manner.…”

Section: Derivation Via the Path Integralsupporting

confidence: 83%

“…It should be emphasized that the factor of p 2 ℓ in equation (12) was not an ad hoc choice but in fact a physicallysignificant one, which will become apparent in the context of the path-integral derivation presented in the following section (See the comments following equation (42) for more details).…”

Section: Correspondence Of Statistical/spacetime Eventsmentioning

confidence: 99%

“…The negative binomial distribution (NBD) has served as an especially accurate statistical model for a broad range of multiplicity observations in particle collision experiments, e.g. pp ¯, hh, hA, AA, e + e − [1][2][3][4][5] (See [6] for an overview), and is argued to be a scale-invariant property of matter [7,8], providing the best fit for astronomical observations, where it predicts the number of galaxies in a region of space [9][10][11][12]. Although several theories have been proposed to explain the relevance of the NBD, the precise physical principles behind its occurrence in these observations are unknown [1,2,11,13,14].…”

mentioning

confidence: 99%

“…[19][20][21][22][23][24][25][26]). The distribution function is used to study the probability of observing n galaxies in a number of disconnected, volumetric cells, where the void probability, or zero-point correlation function, which relates all higher-order correlation functions, has received increasing attention as a tool in the field, for which the NBD has proven the most effective [9][10][11][12]. The model can be described as the probability of recording a given number of 'successes' (observing a galaxy) after a certain number of 'failures' (voids), where the probability of a failure depends on the density of the sample and how clustered it is [27].…”

mentioning

confidence: 99%

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Significance of the negative binomial distribution in multiplicity phenomena

Tezlaf

2023

Phys. Scr.

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The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of quantum-scale events in particle collision experiments and predicting the prevalence of cosmological observables, such as the number of galaxies in a region of space. Despite its widespread applicability and empirical success in these contexts, a theoretical justification for the NBD from first principles has remained elusive for fifty years. The accuracy of the NBD in modeling hadronic, leptonic, and semileptonic processes is suggestive of a highly general principle, which is yet to be understood. This study demonstrates that a statistical event of the NBD can in fact be derived in a general context via the dynamical equations of a canonical ensemble of particles in Minkowski space. These results describe a fundamental feature of many-body systems that is consistent with data from the ALICE and ATLAS experiments and provides an explanation for the emergence of the NBD in these multiplicity observations. Two methods are used to derive this correspondence: the Feynman path integral and a hypersurface parametrization of a propagating ensemble.

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“…) ˆ, which is consistent with the definition in equation (12). It is easy to check that 2 z á ñ ˆis also consistently defined in a similar manner.…”

Section: Derivation Via the Path Integralsupporting

confidence: 83%

Section: Correspondence Of Statistical/spacetime Eventsmentioning

confidence: 99%