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.     

Charged particle multiplicity distributions in restricted rapidity intervals inZ0 hadronic decays

The multiplicity distributions of charged particles in restricted rapidity intervals inZ ⁰ hadronic decays measured by the DELPHI detector are presented. The data reveal a shoulder structure, best visible for intervals of intermediate size, i.e. for rapidity limits around ±1.5. The whole set of distributions including the shoulder structure is reproduced by the Lund Parton Shower model. The structure is found to be due to important contributions from 3-and 4-jet events with a hard gluon jet. A different model, based on the concept of independently produced groups of particles, clans, fluctuating both in number per event and particle content per clan, has also been used to analyse the present data. The results show that for each interval of rapidity the average number of clans per event is approximately the same as at lower energies.This paper is dedicated to the memory of Léon Van Hove     

Multiplicity distributions in a thermodynamical model of hadron production ine + e − collisions

Predictions of a thermodynamical model of hadron production for multiplicity distribution ine ⁺ e ^? annihilations at LEP and PEP-PETRA centre of mass energies are shown. The production process is described as a two-step process in which primary hadrons emitted from the thermal source decay into final observable particles. The final charged tracks multiplicity distributions turn out to be of Negative Binomial type and are in quite good agreement with experimental observations. The average number of clans calculated from fitted Negative Binomial coincides with the average number of primary hadrons predicted by the thermodynamical model, suggesting that clans should be identified with primary hadrons.     

A combined model for pseudorapidity distributions in p-p collisions at center-of-mass energies from 23.6 to 7000 GeV

In p-p collisions, the charged particles produced consist of two leading particles and those frozen out from the hot and dense matter created in the collisions. The two leading particles are in the projectile and target fragmentation regions, respectively, which, in this paper, are conventionally supposed to have Gaussian rapidity distributions. The hot and dense matter is assumed to expand according to unified hydrodynamics, a hydrodynamic model which unifies the features of the Landau and Hwa-Bjorken models, and freeze out into charged particles from a space-like hypersurface with a fixed proper time of τFO. The rapidity distribution of these charged particles can be derived analytically. The combined contribution from both leading particles and unified hydrodynamics is then compared against experimental data from a now available center-of-mass energy region from 23.6 to 7000 GeV. The model predictions are consistent with experimental measurements.     

The n-jet inclusive cross-section in the Hard Pomeron model

The inclusive production of several jets is studied in the framework of the hard pomeron model. The average jet momenta are found to be strongly ordered and growing towards the central c.m. rapidity, as expected. Strong positive correlations are found for pairs of jets neighbouring in rapidity, both in the forward-backward and forward-forward directions. Received: 29 September 1997 / Published online: 26 February 1998     

Some remarks on the particle multiplicities

Recent ALICE data for the multiplicity distributions in the central rapidity bins at LHC energies are compared with the results from two default versions of the PYTHIA 8 generator. We find that, contrary to the earlier versions of PYTHIA, the model overestimates the increase of average multiplicity with energy. Tuning two of the model parameters one obtains reasonable agreement with data. The dependence of the normalized moments of the distribution on the rapidity bin width and on energy is also qualitatively correct.     

A Study of Compton Form Factors in Scalar QED

Deeply virtual Compton scattering has been proposed as a tool to study the structure of hadrons in an exclusive process. The Compton-scattering amplitude can be expressed in terms of scalar quantities, the Compton form factors. Their number depends on the spin of the target as well as the virtuality of the incoming and outgoing photons. For high values of the virtuality Q ² of the incoming photon, these form factors are expected to scale with inverse powers of Q ². In this paper these features are studied for a scalar target hadron.     

Superposition models and the multiplicity fluctuations in heavy-ion collisions

A class of simple superposition models based on the Glauber picture of multiple collisions is compared with the data on the centrality dependence of the multiplicity distributions in a central rapidity bin. We show how the results depend on the specific assumptions concerning the distributions in the number of participants and their relations to the distributions of the number of produced hadrons in various phase space bins. None of the versions of the model describes satisfactorily the centrality dependence of the scaled dispersion.     

Asymmetries in semi-leptonic hyperon decay

Based on the thermodynamic model for particle production, inclusive two-particle correlations are studied. The model is used to study integrated correlations R⁽²⁾(s) and rapidity correlations at accelerator and ISR energies.Particle production is described via the formation of clusters called fireballs. The average mass of these clusters changes as $\text{s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>w</mtext>}}\text{exp}\text{(? |η|ν), (0 ? ν, w ? 1)}$ with the primary energy s and fireball rapidity η. The model produces in the limiting cases the same correlations as the multiperipheral model (with w = 0) and the diffractive excitation model (with w = 1) but contains also all intermediate cases (0 < w < 1) in which fireballs increasing in mass and number are formed. The average number of fireballs produced is also calculated. At ISR energies integrated correlations R⁽²⁾ and rapidity correlations are very different in the cases $\text{w = 0,}\text{1}\text{2}\text{and}\text{1}$. Therefore, experimental data at high energy on R⁽²⁾(s) or on rapidity correlations will allow one to determine the parameter w. Measurements of these different quantities should result in a consistent picture for the production of fireballs.     

Theoretical analysis of the ship noise demodulation spectrum harmonic clan feature

The structure law of the ship noise demodulation spectrum harmonic clan feature and corresponding applications to the recognition problem are studied by theoretical derivation and sample analysis.In order to recognize the propeller blade-number,the ship propeller cavitation noise model is established on the basis of five hypotheses.Further,the mathematical expressions of the structure law are deduced by the model.And the class space of the propeller blade-number is analysed mathematically.The results can be applied to target recognition as expert knowledge.Finally,the demodulation spectrum harmonic clans of experiment samples are obtained by using the wavelet packet.The structure law is validated by the statistic analysis of experiment samples.It is shown that the statistical average results of experiment samples are consistent very well with the theory structure law,and 78.6% of the samples basically accord with the theory structure law.     

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 particle production at the ISR interpreted by independent emission of clusters

The magnitude and range of two particle correlations in the central rapidity plateau region are calculated under the assumption that independent emission of clusters and their subsequent decay is the dominant origin of rapidity correlations. Consistency with the data is achieved with clusters decaying into a mean number of 3.0 pions. For rising c.m. energy the average cluster size approaches a limit.     

Kinetics of Active Surface-Mediated Diffusion in Spherically Symmetric Domains

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of Bénichou et al. in (J. Stat. Phys. 142:657, 2011) and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.     

Bose–Einstein study of position–momentum correlations of charged pions in hadronic Z0 decays

A study of Bose–Einstein correlations in pairs of identically charged pions produced in e⁺e^- annihilations at the Z⁰ peak has been performed for the first time assuming a non-static emitting source. The results are based on the high statistics data obtained with the OPAL detector at LEP. The correlation functions have been analyzed in intervals of the average pair transverse momentum and of the pair rapidity, in order to study possible correlations between the pion production points and their momenta (position–momentum correlations). The Yano–Koonin and the Bertsch–Pratt parameterizations have been fitted to the measured correlation functions to estimate the geometrical parameters of the source as well as the velocity of the source elements with respect to the overall centre-of-mass frame. The source rapidity is found to scale approximately with the pair rapidity, and both the longitudinal and transverse source dimensions are found to decrease for increasing average pair transverse momenta.     

SEMI-INCL USIVE DISTRIBUTIONS AND RAPIDITY DEPENDENCE OF MULTIPLICITY DISTRIBUTIONS IN e+e－ ANNIHILATION INTO TWO JETS

In this paper,the rapidity distribution of quarks is further assumed to be a uniform distribution with the constraint of four momentum conservation.We apply Monte Carlo approaches to light quark jets.The semi-inclusive distributions and the multiplicity distributions in rapidity intervals are calculated.The characteristics of these distributions are discussed and the results are compared with the experimental data of average jets.     

Dynamical correlations in the Dual Parton Model

The effect of multiple ‘chain’ contributions to particle production, which appears in the Dual Parton Model at collider energies, is investigated in an exploratory model, in which other sources of correlations are largely neglected. Attention is given to the question of KNO scaling for the multiplicities observed in restricted or unrestricted rapidity ranges. The rapidity distribution associated with a fixed number of particles within a suitably chosen interval, is found to be sensitive to details of the mechanism of multiple chain production.     

原子—场耦合系统中非局域性和纯度

本文讨论了光场初态和热库对原子——场耦合系统中量子非局域性和线性熵的影响。我们发现如果腔场无损耗且处于真空库，原子——场态会周期性的展现量子非局域性，原子和场的线性熵也会周期性地振荡，其周期和量子非局域性变化的周期相同。如果腔场损耗很弱而且热库的平均光子数很小，量子非局域性会消失，原子和场振荡的振幅逐渐减小。量子非局域性消失的速度取决于初始压缩相干态的幅度、腔的衰减系数和热库的平均光子数N。场越强、平均光子数和衰减系数越大，非局域性减弱的越快。     

Gluon saturation and baryon stopping in the SPS, RHIC, and LHC energy regions

A new geometrical scaling method with a gluon saturation rapidity limit is proposed to study the gluon saturation feature of the central rapidity region of relativistic nuclear collisions. The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. We take advantage of the gluon saturation model with geometric scaling of the rapidity limit to investigate net baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions. Predictions for net-baryon rapidity distributions, mean rapidity loss and gluon saturation feature in central Pb+Pb collisions at the LHC are made in this paper.     

The scaling behavior of the molecular parameters of the hyperbranched polymers made by self-condensing vinyl polymerization

The hyperbranched polymers can be made by self-condensing vinyl polymerization without gelation transition. The average molecular weights, as well as the average sizes, can reach infinite values as the reaction is quantitatively completed, and the scaling forms of the molecular parameters should exist. In the paper, based on a recursion formula, the scaling form of the number fraction distribution and the number of the n-mers are given analytically as the conversion of double bonds is near 1. The mean square radius of gyration for very large hyperbranched polymers is calculated explicitly to give a scaling exponent. Finally, a scaling relation associated with the fractal dimension and the polydispersity exponent is given clearly.