Multiplicity distributions from branching equations with constant vertex probabilities.

This paper presents the charged-particle multiplicity distributions for e+e− annihilation at √s =29 GeV measured in the High Resolution Spectrometer. The data, which correspond to an integrated luminosity of 185 pb−1, were obtained at the SLAC e+e− storage ring PEP. The techniques used to correct the observed prong numbers are discussed. The multiplicity distribution of the charged particles has a mean value 〈n〉=12.87±0.03±0.30, a dispersion D2=3.67±0.02±0.18, and an f2 moment of 0.60±0.02±0.18. Results are also presented for a two-jet sample selected with low sphericity and aplanarity. The charged-particle distributions are almost Poissonian and narrower than have been reported by other e+e− experiments in this energy range. The mean multiplicity increases with the event sphericity, and for the sample of threefold-symmetric three-jet events, a value of 〈n〉=16.3±0.3±0.7 is found. No correlation is observed between the multiplicities in the two hemispheres when the events are divided into two jets by a plane perpendicular to the thrust axis. This result is in contrast with the situation in soft hadronic collisions, where a strong forward-backward correlation is measured. For the single jets, a mean multiplicity of 6.43±0.02±0.15 and a dispersion value of D2=2.55±0.02±0.13 are found. These values give further support to the idea of independent jet fragmentation. The multiplicity distributions are well fit by the negative-binomial distribution. The semi-inclusive rapidity distributions are presented. Comparisons are made to the measurements of charged-particle multiplicities in hadron-hadron and lepton-nucleon collisions.Received 12 May 1986DOI:https://doi.org/10.1103/PhysRevD.34.3304©1986 American Physical Society

The negative binomial distribution (NBD) is fitted to all charged and to negative particle multiplicity distributions in restricted rapidity intervals, both in the forward and backward c.m. hemispheres of positive meson interactions on Al and Au nuclei. For negative particle multiplicity distributions, the NBD parameters are also determined as a function ofng, the number of grey tracks, corresponding to varying number of intranuclear collisions. The data are interpreted in terms of the clan picture of Giovannini and Van Hove and compared to the MCMHA and Fritiof models. Both models reproduce quite well the global multiplicity distributions, but not when sub-samples are considered with fixed number of grey tracks. Regularities are better visible on the parton than on the particle level.

The method of normalized factorial moments has been used extensively to study the fluctuations in pseudorapidity of charged particle multiplicity as a function of the interval δη. Experience in analyzing the data from light and heavy ion collisions in terms of distributions rather than moments suggests that conventional fluctuations of multiplicity and transverse energy can be well described by gamma or Negative Binomial Distributions (NBD). Multiplicity distributions from central (ZCAL) collisions of 16 O+Cu at 14.6 A GeV/c have been analyzed by the E802 collaboration as a function of the interval δη≥0.1 in the range 1.2≤η≤2.2. Excellent fits to NBD were obtained in all δη bins. The k parameter of the NBD fit exhibits a steep linear increase with the δη interval, which due to the well known property of the NBD under convolution, indicates that the multiplicity distributions in adjacent bins of pseudorapidity δη~0.1 are largely statistically independent. This result explains and demystifies “intermittency.”

On the origin of negative binomial multiplicity distributions in proton-nucleus collisions

Two-component model in quantum statistical framework compared with multiplicity distributions in proton–proton collisions at energies up to [formula omitted

This work studies the validity of the negative binomialdistribution in the multiplicity distribution of chargedsecondaries in 16O and 32S interactionswith AgBr at 60 GeV/c per nucleon and 200 GeV/cper nucleon, respectively. The validity of negative binomialdistribution (NBD) is studied in different azimuthal phase spaces.It is observed that the data can be well parameterized in termsof the NBD law for different azimuthal phase spaces.

The correspondence between the moments of distribution of primary particles total multiplicity and the moments of partial distribution of charged hadrons multiplicity is obtained. This dependence permits to describe the data on the charged hadrons multiplicity moments by means of negative binomial distribution (NBD) for total hadron multiplicity. The NBD parameterk is fitted as a rational function of c.m. energy.

This review summarizes and critically reviews measurements of charged-particle multiplicity distributions and pseudorapidity densities in collisions between and . Related theoretical concepts are briefly introduced. Moments of multiplicity distributions are presented as a function of . Feynman scaling, KNO scaling as well as the description of multiplicity distributions with a single negative binomial distribution and with combinations of two or more negative binomial distributions is discussed. Moreover, similarities between the energy dependence of charged-particle multiplicities in and e+e− collisions are studied. Finally, various predictions for pseudorapidity densities, average multiplicities in full phase space and multiplicity distributions of charged particles in collisions at the LHC energies of and 14 TeV are summarized and compared.

We report on an analysis of the multiplicity distributions of charged particles produced ine+e− annihilation into hadrons at c.m. energies between 14 and 46.8 GeV. The charged multiplicity distributions of the whole event and single hemisphere deviate significantly from the Poisson distribution but follow approximate KNO scaling. We have also studied the multiplicity distributions in various rapidity intervals and found that they can be well described by the negative binomial distribution only for small central intervals. We have also analysed forward-backward multiplicity correlations for different energies and selections of particle charge and shown that they can be understood in terms of the fragmentation properties of the different quark flavours and by the production and decay of resonances. These correlations are well reproduced by the Lund string model.

In this study, the charged particle multiplicity distribution produced in anti-neutrino and neutrino-nuclear emulsion interactions is studied in terms of negative binomial distribution in varying invariant mass of the hadronic system intervals for the first time. Many articles have shown that the negative binomial distribution is very useful in describing and interpreting the multiplicity of experimental data in the literature. For this reason, a similar study is conducted on neutrino and anti-neutrino interactions to better understand the particle production mechanism. Experimental data for the analysis are obtained from the CHORUS Collaboration paper on the production of charged particles in anti-neutrino and neutrino-nuclear emulsion interactions at high energy. For multiplicity distributions of both interactions, the invariant mass of the hadronic system intervals is defined as given in the CHORUS Collaboration article. Then the negative binomial fit is applied to the experimental data for each energy range. In terms of chi-square values for both interactions, a good agreement has been observed between the experimental data and their fit in each energy range. The results of applied fits are shown through figures and tables, presenting the obtained chi-square values, free parameters, and their energy dependence.

There are several parametric models to describe the charged particle multiplicity distributions in literature. Among them, log-normal distribution and negative binomial distribution are the most well-known parametric models. In this study, negative binomial and log-normal distributions are compared and tested in neutrino interactions produced in DONUT experiment. This analysis was carried out using the real experimental results of the DONUT Collaboration. The results of the analysis show that the neutrino data, reported by DONUT collaboration, is well described by negative binomial and log-normal distribution. In terms of fit parameters, the χ/ndf value of the both distribution NBD and LND are close to unity but log-normal distribution data slightly better than negative binomial distribution.

In this paper we investigate how a finite detection efficiency affects three\npopular multiplicity distributions, namely the Poisson, the Binomial and the\nNegative Binomial distributions. We found that a multiplicity-independent\ndetection efficiency does not change the characteristic of a distribution,\nwhile a multiplicity-dependent detection efficiency does. We layout a procedure\nto study the deviation of moments and their derivative quantities from the\nbaseline distribution due to a multiplicity-dependent detection efficiency.\n

Multiplicity distributions of charged particles produced in interactions of 800 GeV protons with emulsion nuclei in various rapidity windows are presented. The data is also analyzed separately for the forward and the backward hemispheres, for rapidity windows of different widths. It is found that the Negative Binomial Distribution (NBD) describes well the multiplicity distribution of secondary particles in various rapidity windows and also in both the hemispheres. We have compared the NBD parameters, in both the hemispheres, at 200 GeV and 360 GeV, with those at 800 GeV. The behaviour of NBD parameters in rapidity windows of different widths and for different targets has also been studied.

A new statistical description of hardonic and e +e − multiplicity distributions

On statistical mechanics developments of clan concept in multiparticle production