Description of local multiplicity fluctuations and genuine multiparticle correlations

Abstract

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.

Fractal Structure of Hadrons: Experimental and Theoretical Signatures

“…The fractal dimension obtained in intermittence analysis from pp collisions is in the range 0.43 to 0.65 [23][24][25][26][27]. Such analyses are rather complex and delicate, with many factors that can disturb the results [28,29]. The limitations of this approach were already recognized by the beginning of the new millenium.…”

“…As usual, the limit q → 1 reduces to the Boltzmann statistics, and from Equations (26) and (27) it is possible to see that this limit corresponds to τ << T; therefore, the internal energy, E, is much smaller than the kinetic energy, F, which corresponds to an ideal gas in the Boltzmann statistics. Furthermore, Equation (28) shows that the use of the q-exponential factor-instead of the exponential one that appears in Boltzmann statistics-allows a direct application of Thermodynamics rules to calculate all necessary quantities without worrying about the complexities of the thermofractal structure.…”

Azimuthal Anisotropy in High-Energy Nuclear Collision: An Approach Based on Complex Network Analysis

“…This has already been confirmed mathematically in [4]. Sarkisyan [5] has analysed the parametrization of multiplicity distributions of the produced hadrons in high-energy interaction to describe higher order genuine correlations [6], and established the necessity of incorporating the multiparticle correlations with the property of self-similarity to achieve a good description of the measurements. Wang et.…”

Genuine correlations of like-sign particles in hadronic Z0 decays

“…Comparing to the data, we conclude that the multiplicity distribution of all charged particles, as well as that of like-sign particles, deviates strongly from a Negative Binomial in small phase space domains. For further discussion, in the present context, of this and other much studied multiplicity distributions we refer to [38].…”