H-function extension of the NBD: further applications

Hegyi, S.

doi:10.1016/s0370-2693(97)01329-4

Cited by 7 publications

(6 citation statements)

References 17 publications

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“…Among them scenarios with the fluctuation of N in the Poisson distribution (formally correspond to the so called Poisson transforms) seem to be very promising. It is remarkable that fluctuation of N in the Poisson distribution, with f ( N ) given by the generalized gamma distribution, leads to fractional negative binomial distribution (known also as HNBD, because such extension of NBD can be expressed in terms of the Fixs H-function) which demonstrates oscillatory behavior of the corresponding combinants [35][36][37][38]. Despite that in the HNBD we have P (0) < P (1), such extension of NBD (with only one additional parameter) is worth future detailed study.…”

Section: Discussionmentioning

confidence: 99%

Intriguing properties of multiplicity distributions

2019

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Section: Discussionmentioning

confidence: 99%

Intriguing properties of multiplicity distributions

2019

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“…at µ > −1. This disagreement can be assigned to different regions of the parameter k, found to be large (k → ∞) in the case of the full-multiplicity distribution studies [61,65] while having finite values in our investigation (vide infra). important differences.…”

Section: Comparison With Opal Measurements and Discussionmentioning

confidence: 65%

“…12 It is interesting to note that being limited to like-charged particles, a study of particle bunching is less dependent on correlations induced by charge conservation (and partly by resonance production), in addition to the above-mentioned advantage of such a study to be less affected by the energy-momentum constraints [57]. 13 Our observation contradicts the property of the factorial moments and cumulants shown [61,65] to oscillate around zero at |µ| > 1 and not e.g. at µ > −1.…”

Section: Comparison With Opal Measurements and Discussionmentioning

confidence: 76%

“…Comparing the results obtained to the HNB studies [61,62,65] of the LEP data and, particularly, to that of the uds-quark jets [64] (see also Sect. 2), one can see similarities as well as important differences.…”

Section: Comparison With Opal Measurements and Discussionmentioning

confidence: 77%

“…In e + e − annihilations, it was found that HNB describes the data below the top PETRA energies for µ < −1 and k = 1 [65], whereas at high energies the HNB description favour µ ≈ 0 and large k [61,62,64]. The latter, as well as the above mentioned success of the 6 See footnote 2.…”

Section: Normalized Factorial Moments and Cumulants From Various Para...mentioning

confidence: 98%

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Description of local multiplicity fluctuations and genuine multiparticle correlations

Sarkisyan

2000

Physics Letters B

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Various parametrizations of the multiplicity distribution are studied using the recently published large statistics OPAL results on multidimensional local fluctuations and genuine correlations in e + e − → Z 0 → hadrons. The measured normalized factorial and cumulant moments are compared to the predictions of the negative binomial distribution, the modified and generalized versions of it, the log-normal distribution and the model of the generalized birth process with immigration. This is the first study which uses the multiplicity distribution parametrizations to describe high-order genuine correlations. Although the parametrizations fit well the measured fluctuations and correlations for low orders, they do show certain deviations at high orders. We have shown that it is necessary to incorporate the multiparticle character of the correlations along with the property of self-similarity to attain a good description of the measurements. * Email address: edward@lep1.tau.ac.il 1 Earlier, using correlation (strip) integrals to reduce statistical errors, multiparticle genuine correlations have been searched for in hadron-hadron [9,10] and lepton-hadron [11] interactions. It is worth to note that except for problems arising due to various possibilities in defining of a proper topology of particles and a distance between them (see e.g. [2]), a rather important difficulty in interpreting results could come from a translation invariance breaking of the many-particle distributions [12]. This will lead to different results on moments/cumulants according to a variable used because different variables are sensitive to different hadroproduction mechanisms [12,13]. For example, in the high-order genuine correlations obtained in Ref. [9,11] the study is performed in four-momentum difference squared, Q 2 , dependent on Bose-Einstein correlations, whereas in the pseudorapidity analysis [10] no correlations higher than two-particle ones were found, since (pseudo)rapidity seems [13] to be more "natural" variable to search for jet formation than e.g. for Bose-Einstein correlations.

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Development of particle multiplicity distributions using a general form of the grand canonical partition function

Lee¹,

Mekjian²

2004

Nuclear Physics A

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Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a, x, z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ . Various physical phenomena such as hierarchical structure, void scaling relations, KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ . Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given. It is shown that just looking at the mean and fluctuation of data is not enough to distinguish these distributions or the underlying mechanism. The mean, fluctuation and third cummulant of distribution determine three parameters x, z, a. We find that a generalized random work model fits the data better than the widely used negative binomial model.

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H-function extension of the NBD: further applications

Abstract: The H-function extension of the Negative Binomial Distribution is investigated for scaling exponents mu<0. Its analytic form is derived via a convolution property of the H-function. Applications are provided using multihadron and galaxy count data for P(n).Comment: 6 pages REVTeX, 3 figure

Cited by 7 publications

References 17 publications

Intriguing properties of multiplicity distributions

Intriguing properties of multiplicity distributions

Description of local multiplicity fluctuations and genuine multiparticle correlations

Development of particle multiplicity distributions using a general form of the grand canonical partition function

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