High order moments of the\bar p p multiplicity distribution in the dual parton model

The first four moments of the \(\bar p\) p multiplicity distribution are computed in the framework of the dual parton model at ISR, SPS collider and Tevatron energies, and for different rapidity intervals. Our results exhibit a striking dependence of the various moments on the size of the rapidity interval which is characteristic of the nature of the rescattering chains in the dual parton model. They also show a violation of KNO scaling throughout the considered energy range. Our results indicate that only light clusters (consistent with known resonances) are produced at all energies.     

Charged particle multiplicity distributions ine + e − annihilation at 29 GeV: a comparison with hadronic data

The charged particle multiplicity distributions for two-jet events ine ⁺ e ^? annihilation at 29 GeV have been measured using the High Resolution Spectrometer at PEP. A Poisson distribution describes the data for both the complete event and for the single jets. In addition, no correlation is observed between the multiplicities in the two jets of an event. For fixed values of the prong number of the complete event, the multiplicity sharing between the two jets is in good agreement with a binomial distribution. The rapidity gap distribution is exponential with a slope equal to the mean rapidity density. These observations, which are consistent with a picture of independent emission of single particles, are contrasted to the results from soft hadronic collisions and conclusions are drawn about the nature of clusters.     

Higher moments of the pion multiplicity distribution in proton-proton interactions at 12 and 24 GeV/c

Results on higher moments of the pion multiplicity distribution are presented for pp interactions at 12 and 24 GeV/c incident lab momentum. A simple parametrization for the pion multiplicity distribution is established at 12 and 24 GeV/c and is then used to discuss the energy dependence of higher moments in a range from 4 to about 500 GeV/c incident lab momentum.     

Experimental study of proton-emulsion nuclei interactions at high energy

Proton-emulsion nuclei interactions at 200 and 400 GeV have been studied. The results on the energy dependence of <n _s(n _s-1)> and <n _s>/D, multiplicity scaling, multiplicity density scaling in the central region, integral angular distribution, rapidity dispersion and maximum rapidity gap are presented and compared with those of proton-nucleon interactions at the corresponding energies.     

Fluctuations of multiplicities in rapidity windows in sulphur-sulphur collisions at 200A GeV

Multiplicity distributions and their second moments fornegatively charged particles produced in³²S-S central and minimum bias interactions at 200A GeV are studied in various rapidity intervals. Fritiof and Venus models mostly describe the dependence of second moments on rapidity intervals in minimum bias interactions, but not in central collisions. For central collisions the behaviour of second moments might indicate enhanced multiplicity fluctuations.     

Hadron production ine +e− annihilation and μ-p collisions under the assumption of longitudinal phase space dominance

Rapidity and multiplicity distributions are calculated for the hadrons produced ine ⁺e^? annihilation and deep inelastic muon-proton collisions for c.m. energies of 10 to 40 GeV. The hypothesis of longitudinal phase space dominance leads to a probability distribution which is identical to that of a grand canonical ensemble of non-interacting particles. We successfully describe experimental rapidity distributions, domains of Feynman-x scaling and scaling violations and the rapidity dependence of the mean transverse momentum. Multiplicity distributions are derived to be close to negative binomial distributions even for finite rapidity intervals. The plateau in the rapidity distribution is the origin for the negative binomial distribution in multiplicity. The mean number of hadrons of each species and the mean overall transverse momentum are the main input parameters in our calculation and are taken from experiment.     

The rapidity distribution of the cascade inside deuteron in πd high energy collisions

The problem of the existence of internuclear cascade and its characteristics are analysed in the π^? d experiment at 205 GeV/c. Two versions of the additive quark model are used to obtain the mean multiplicity and the rapidity distribution of charged particles produced through cascading. It is shown that the cascading effect does exist. The particles produced through this effect have the rapidity distribution very similar as in elementary low energy hadron-nucleon interactions. Both the rapidity distribution and the mean multiplicity do not depend on the version of the additive quark model which was used to obtain them.     

Multiplicities in electroproduction and e+e− annihilation

It is shown how more sophisticated versions of the parton model can replace the naive expectation of final state hadrons being produced in ep or e⁺e^? collisions in two jets of finite multiplicity, well-separated in rapidity, with a picture that permits the rapidity gap to be filled in and allows the multiplicity to rise with energy, even up to the limit imposed by energy conservation. Large multiplicity is shown to imply a rather slow approach to scaling and a significant tail in the transverse momentum distribution.     

A constituent quark model for particle production in collisions between hadrons

It is shown that a constituent picture of hadrons, with no other fundamental assumption than that only one constituent in each hadron interacts with one constituent in the other hadron, explains several features of particle production in high-energy collisions. We obtain KNO scaling of the particle multiplicity, a neutral for multiplicity for fixed charged multiplicity which is independent of the energy, and a rapidity distribution of the central fireball which depends on n/〈n〉 only. Numerical applications show that the quark momentum distribution which reproduces the experimental data in strong interactions is very similar to the valence quark momentum distribution derived from deep inelastic scattering experiments.     

Study of correlation effects in high-multiplicity proton-proton reactions at 12 and 24 GeV/c

In this paper we study correlations in multiparticle final states from pp interactions at 12 and 24 GeV/c. In an attempt to distinguish true dynamical correlations from the consequences of kinematics together with P_T damping and the leading-particle effect, we compare the data with an independent-emission model which reproduces the single-particle spectra and also with a model that simulates a fragmentation mechanism. We investigate the forward-backward particle configurations and in particular the multiplicity imbalance and charge transfer, defining forward-backward by the largest rapidity gap as well as simply by c.m.s. hemispheres. We also study clustering by looking at distributions of the dispersions in longitudinal rapidity. From the comparison of the data with the models we find clear evidence for dynamical correlations of a sort one would expect from fragmentation-type mechanisms. We also find indications of non-fragmentation formation of neutral meson clusters.     

Signal for intermittency in e+e− reactions obtained from negative binomial fits

With a simple relation between the parameter k of the negative binomial distribution and the factorial moments 〈Fⁱ〉 we reanalyse published data from e⁺e⁻ reactions at √s=29 GeV on multiplicity distributions in rapidity bins to show that there is a significant rise of the 〈Fⁱ〉 with decreasing bin size δy along the thrust axis. The rise for δy<1 can be regarded as a signal for intermittency. For further discussion we compare the data with the Lund shower Monte Carlo. We suggest a direct measurement of factorial moments in e⁺e⁻ jets.     

Correlation studies in quark jets using combinants

A brief summary of the basic properties of combinants is provided. Their behavior is analysed using the Opal multiplicity data for light quark jets in restricted rapidity bins. For |Δy|≤1 the combinants do not exclude clustering effects with Poisson superposition. For |Δy|≤2 this pattern of correlations is ruled out by the sign-changing oscillations of combinants, as well as other models which predict oscillations alternating in sign. The future experimental possibilities concerning combinants are discussed.     

Self-similarity in one and two dimension of 800 GeV proton interactions with AgBr nuclei

The normalized multiplicity moments in one and two dimensions were investigated for secondary particles produced in 800 GeV proton interactions with AgBr nuclei in nuclear emulsion. The fluctuations are found to be more in two dimensions as compared to one dimension. It has been shown that the self-similar cascade model describes well the observed fluctuations. The multiplicity shows a weaker dependence of moments for high multiplicity events in comparison to all multiplicity events. The slope ratios (r _q) are not different in one and two dimensions and are found to be independent of the multiplicity. Ther _q distribution is well represented by the logbinomial and Levy-stable distributions which follows from the self-similar cascade model.     

Multiparticle production in hadron-nucleus collisions around 100 GeV

Experimental results of various groups are analysed in order to establish empirical laws on how the multiplicity and rapidity distributions of produced particles depend on the nature of the projectile hadron, its energy E and on the number v of struck nucleons. Global observables of these distributions (mean multiplicity, mean rapidity and variances) are parametrized. The parameters which govern the effects of multiple scattering are found independent of the energy E and of the nature of the hadron. Then, using identical hadron-nucleon input data, we evaluate the predictions of eight theoretical models and compare them with the empirical laws. Some models can be ruled out, while others, though based on very different physical assumptions, are compatible with experiment.     

Rapidity correlations in π+ p,K + p andpp interactions at 250 GeV/c

Two- and three-particle rapidity correlations are analyzed inK ⁺ p and π⁺ p-interactions at 250 GeV/c. The main contribution to the two- and three-particle correlation functions comes from mixing of events of different multiplicity. The (short range) two-particle correlation remaining after exclusion of mixing is significantly larger for (+?) than for the equal charge combinations, and is positive for a wider range in rapidity difference. FRITIOF and a 2-string DPM are excluded by our data. A quark-gluon (multi-)string model can describe our inclusive correlation function, but needs to be tuned on the short range part. The multiplicity mixing part increases much faster with increasing energy than the short range part. In the central region, our correlation is similar to that observed ine ⁺ e ^? and μp collisions at similar energy.     

Negative binomials and multiplicity distributions in 250 GeV/cK + and π+ interactions on Al and Au nuclei

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 ofn _g, 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.     

Forward-backward multiplicity distributions in the Peřina-McGill scheme and analysis ine + e − collisions

A forward-backward multiplicity correlation is considered by the use of the Pe?ina-McGill formula. We obtain analytic formulae for conditional cumulants of the backward multiplicity and a conditional backward multiplicity distribution at a given forward multiplicity. The multiplicity distribution and the conditional mean multiplicity observed at \(\sqrt s = 29\) in HRS ine ⁺ e ^? collisions are analysed. We predict the conditional moments and the conditional backward multiplicity distribution. Those should be compared with the future analyses in HRS.     

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.