Truncated Compound Poisson (TCP) alternative to multiplicity distribution in Hadron-Hadron collisions

On using the Poisson distribution truncated at zero for cluster decay in a compound Poisson process, we obtain TCP distributions which describe quite well the hadronic multiplicity data in hadron-hadron collisions. A comparison is made between TCP and negative binomial distributions for UA5 data.     

Negative binomial multiplicity distributions and intranuclear cascade

The multiplicity distribution of the ejected particles, as predicted by the intranuclear cascade model, are analyzed in terms of negative binomial shapes, which have recently been shown to be relevant for high-energy collisions. We discuss some physical features which are related to this distribution shape.     

Negative binomial multiplicity distributions for proton-nucleus collisions from a string model

Multiplicity distributions of charged particles produced in collisions of ultrarelativistic protons with nuclei are studied in a string model. Recently measured multiplicity distributions in proton-nucleus reactions display a negative binomial shape. The string model VENUS reproduces the data well. We trace back within the model the origin of the negative binomial form of the multiplicity distributions. We find that the final multiplicity distribution can be expressed as a continuous superposition of Poisson distributions with different mean multiplicities ∫dNW(N)P(N, n). The Poisson distribution represents the string fragmentation, whereas the weight factorW(N) reflects the string mass distribution. This quantity has contributions due to both the nuclear structure and the parton structure of nucleons. We show thatW(N) is very well approximated by a gamma-distribution . This leads to a negative binomial distribution \(\mathcal{N}(k,\bar N;n)\) with the same parameters as for . It is shown that the fluctuations in the multiplicity are dominated by the string fragmentation fluctuations for small rapidity intervals and by string mass and number fluctuations for large rapidity windows.     

Negative binomial distributions in different pseudorapidity windows in 800 GeV proton-nucleon interactions

Experimental results on multiplicity distributions for full phase space and in different pesudorapidity windows of charged secondary particles produced in proton-nucleon collisions at 800 GeV are presented and discussed. It is found that all these multiplicity distributions are well described by negative binomial distributions. We interpret our results on the basis of clan model. The bin size dependence of multiplicity distribution of charged secondary particles in proton-nucleon interactions is analysed in terms of multifractals. The values of generalised dimensions obtained from fitted distributions show a good agreement with those obtained from the data.     

Masses for clans introduced to explain hadronic multiplicity distributions

The facts that the negative binomial distribution very well describes high energy multiplicity distributions and that this distribution is the result of a compound Poisson-logarithmic distribution are used to search for new dynamics in particle production. It is shown that the logarithmic distribution for the particle multiplicity of clans follows if 1) the number of particles in the clans follows a Poisson distribution at fixed mass and 2) the mass distribution belongs to a certain class of distributions. Data are used to set limits on possible mass distributions. Comparisons with data are made for two examples of distributions.     

Negative binomial distributions and clan model in proton-nucleus interactions

Experimental results on multiplicity distributions in different pseudorapidity intervals of charged shower particles produced in proton-AgBr and proton-CNO collisions at 800 GeV are presented. The different distributions are described well by the negative binomial form. We successfully interpret our results in terms of the clan model. The values of the rapidity gap probability in terms of average number of clans in different pseudorapidity intervals are also determined.     

A note on possible interpretations of negative binomial multiplicity distributions

Different interpretations of negative binomial multiplicity distributions in high-energy hadronic collisions are briefly discussed. It is shown that the interpretation in terms of independent emission of clusters does describe the data well but does not imply early asymptotic behaviour in the average number of clusters, contrary to previous suggestions. In âddition, an alternative interpretation in terms of a continuous superposition of independent emission processes is shown to also describe the data well. Finally, some consequences of extrapolating the presently successful parametrization are discussed.     

The determination of total multiplicity distribution ine + e − annihilation via charged hadron multiplicity distribution

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.     

Z0能区正负电子湮没强子多重数分布及有关参数

对91.1—91.3GeV正负电子湮没带电强子多重数的负二项式分布的适用性及其有关参数、多重数前后关联、集团模型参数、半单举快度分布和反映喷注横动量特点的海鸥图的结果进行了报道.特别对有限快度区的上述有关参数的特点进行了分析,并与多重产生中的唯象模型的理论结果进行了比较.所述实验结果由LEP上ALEPH国际合作组的5万个Z⁰事例得到.     

Hadron Multiplicity Distributions and the Related Parameters in e+e－ Annihilation at Z0 Energy Region

The adaptability of charged hadron multiplicity distributions fitted with negative binomial and its related parameters,forward-backward multiplicity correlation,parameters of clan model,semi-inclusive rapidity distribution and the seagull plots describing the characteristics of transverse momenta of jets are discussed. In particular,the above mentioned parameters in restricted rapidity intervals are analysed and comparde with theoretical results of some phenomenological models of multiparticle production. Most of the results are obtained from 50000 Z⁰ events of ALEPH Collaboration at LEP.     

Evolution of clans in multiparticle production

An alternative interpretation of the development of the clan structure arising formally from the natural decomposition of the negative binomial multiplicity distribution is presented here. Our approach is based on stochastico-physical ideas of multiple production on the parton level. Specific differential-difference evolution equations have been proposed which besides the elementary processes involving the ingredients of QCD branching describe collective phenomena of clan's collapsing and clan's coherent disintegration.     

Renormdynamics, negative binomial distribution, and Riemann zeta function

Renormdynamic equations of motion and their solutions are given. New equation for negative binomial distribution and Riemann zeta function invented.     

Multiplicity distribution of strange particles in heavy ion collisions

We study the multiplicity distribution of strange particles in a hadronic gas constrained by exact strangeness conservation. The multiplicity distribution obtained is narrower than both the Poisson and negative binomial distributions. Correlations among strange particles are also discussed. The results presented might be useful in determining the thermodynamic parameters (volume, temperature and baryon density) of a hadronic gas possibly formed in relativistic nuclear collisions.     

Possible evidence for deconfinement in hadron collisions

The collision of hadrons at very high energies produces an entity whose energy density is extremely large resulting in the emission of a large number of hadrons. Though the entity may not have transited into the deconfined parton phase, the very high energy density may cause more than one charged hadron to be emitted at any instant. This yields a new multiplicity distribution, termed the GS distribution which fits the data as well as the popular negative binomial distribution. Neither the GS nor the NB distribution alone agrees with the data beyond 200 GeV, but a weighted sum of GS and NB distributions fits the experimental results exceedingly well. Since the negative binomial distribution arises from the branching of partons, we interpret the increase with energy of the negative binomial component in the weighted sum as the onset of a deconfined phase. The rising cross section for the negative binomial component parallels very closely the inclusive cross section for hadron jets which also is considered a consequence of parton branching.     

Forward-backward multiplicity correlation in high energy hadron-hadron collisions

The forward-backward multiplicity correlation over the full pseudorapidity range forpp andp \(\bar p\) collisions at ISR and Collider energies have been analysed in terms of a Chou-Yang Type multiplicity distribution which consists of a stochastic (binomial) component forz=n _F ?n _B and a nonstochastic (negative binomial) component forn=n _F +n _B . Reasonable agreement with experimental data is obtained if the final-state particles are assumed, in a cluster model, to be created by the decay of clusters with a mean cluster size (charged particles per cluster) which is energy-dependent.     

Phase space dependence of the multiplicity distribution in π+ andpp collisions at 250 GeV/c

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.     

Clan structure analysis and rapidity gap probability

Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability atTevatron andHera.     

Statistical properties of the nonlinear negative binomial state

In this context, we introduce and investigate the properties of the nonlinear negative binomial state (the state which interpolates between the nonlinear coherent and the number states). Mainly we concentrate on the statistical properties for such state where we have discussed two different cases of squeezing phenomenon. The first case is the normal squeezing while the second is the amplitude squared squeezing, further the second order correlation function is also considered. Our discussion have been extended to include the quasi-probability distribution functions (W-Wigner and Q-functions). The quadrature distribution and the phase properties in Pegg-Barnett formalism besides the phase variances are considered. Examination of the resonance fluorescence against the present state is given (single atom and thermodynamic limit). It has been shown that the atomic inversion is sensitive to any variation in the nonlinear negative binomial number m.