Multiple Refinable Distributions: Existence and Factorization

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 experimental multiplicity and angular distribution of the secondary particles of high-energy nuclear interactions are analysed. The manner in which the estimate of dispersion σ of the log tg θ representation of the angular distribution of the secondaries varies with the energy of the primary, is studied. Based on the observed results, a distribution function which explains both the σ and multiplicity distributions is suggested. By appropriate application of that empirical relation to the «fireball model», the distributions of the mass and Lorentz factor of the fireball are derived.

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

The charged particle multiplicity distribution has been studied for non-single-diffractive π+ p andpp collisions at\(\sqrt s = 22\) GeV, for full phase space as well as for intervals in rapidity, azimuthal angle and transverse momentum. In general, the multiplicity distribution is well described by a negative binomial. From comparison of the distribution for negative or positive particles to that of all charged particles, cascading is favoured as an interpretation over stimulated emission. Interesting consequences follow from a comparison of our results to those at collider energies and toe + e − data at comparable energy. Furthermore, evidence is given that the multiplicity distribution is not exactly of negative binomial type in every (connected or disconnected) phase space region.

Studies of fast protons produced in the reactions of 16O Nuclei incident on emulsion nuclei at 3.7A GeV

In this work we study the multiplicity distributions (MDs) of charged particles within jets in proton-proton collisions, which were measured by the ATLAS Collaboration in 2011, 2016 and 2019. The first dataset refers to jets with smaller transverse momenta (4<pT<40 GeV) whereas the other two refer to higher pT jets (0.1<pT<2.5 TeV). We find that the lower pT set shows no sign of KNO scaling and that the higher pT sets gradually approach the scaling limit. For the lower pT set the mean multiplicity as a function of pT can be well-described by expressions derived from QCD with different approximation schemes. For higher (>500 GeV) values of pT these expressions significantly overshoot the data. We show that the behavior of the MDs can be well-represented by a sub-Poisson distribution with energy dependent parameters. In the range 40<pT<100 GeV there is a transition from sub to super Poissonian behavior and the MD evolves to a geometric distribution, which shows KNO scaling. In this way we fit the MDs in all transverse momentum intervals with one single expression. We discuss the implications of this phenomenological finding. Published by the American Physical Society 2024

We have studied rescattering in 100-GeV/c proton and positive-pion interactions with deuterons in the Fermilab 30-in. bubble chamber. We study specifically events in which the deuteron breaks up and meson production occurs. After attempting to take account of elastic rescattering, we determine the fraction of events in which rescattering occurs, and the multiplicity distribution of the rescatter events. The rescatter fraction found for 100-GeV/c ..pi../sup +/d events is consistent with the values found in 21-GeV/c and 205-GeV/c ..pi../sup -/d experiments while the fraction found for 100-GeV/c pd events is slightly larger. The multiplicity distributions in the rescatter events are in reasonable agreement with 205-GeV/c pp or ..pi../sup -/p multiplicity distributions. We compare our results to predictions of energy-flux-cascade and coherent-tube models.

We present multiplicity distributions which are solutions to branching equations, based on the assumption that the shapes and energy dependence of multiplicity distributions are principally determined by hard parton scattering and subsequent branching. We consider the four processes g\ensuremath{\rightarrow}gg, q\ensuremath{\rightarrow}qg, g\ensuremath{\rightarrow}qq\ifmmode\bar\else\textasciimacron\fi{}, and in a few cases g\ensuremath{\rightarrow}ggg. All vertex probabilities for these processes are taken to be constant. In this simple approximation, we find that Koba-Nielsen-Olesen scaling is systemically violated. We compare the properties of branching distributions with the properties of the widely used negative-binomial distribution and of the stochastic approach.

We analyze the largest set of fragment coincidence data at present available, that of the preceding paper. This set contains all projectile fragments 6\ensuremath{\le}Z\ensuremath{\le}65 produced in 6610 events of Au+Ag and Au+CR-39. We introduce a classification scheme based on the number of heavy fragments in order to define multifragmentation, spallation, and fission events. The multiplicity distribution P(${\mathit{m}}_{\mathit{Z}}$) is Poissonian, and the mean multiplicity as a function of Z can be described either by a power law or by an exponential. The slopes are independent of the projectile energy but depend on the target. While all investigated observables indicate that the multifragmentation in the case of a Ag target is a statistical process, we observe angular correlations in the case of the CR-39 target which indicate that probably the geometry and not the excitation energy is essential. Charge correlations are strong and only partially understood as yet. We find no positive sign for a liquid gas phase transition.

The multiplicity distribution is described in terms of models incorporating the stochastic branching of quarks and gluons, along with fluctuations in their production. Results show a reasonable description of charged-particle multiplicity distributions measured in pp collisions by the CMS collaboration at centre-of-mass collision energies of 0.9, 2.36, and 7 TeV for |η | < 0.5, 1.0, 1.5, 2.0, and 2.4. A prediction for 13 TeV is also given.

A two-channel Chew-Pignotti-type multiperipheral model previously explained some of the clustering effects found in the production of hadrons at high energies. Here the model is successfully compared to the experimental $\mathrm{pp}$ multiplicity distributions at high 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.

Multiboson Effects in Bose–Einstein Interferometry and the Multiplicity Distribution

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.