An impact-parameter model for multiplicity distributions

We study a model for hadron-hadron scattering in which at each value of impact parameter the multiplicity follows a Poisson distribution whose mean is determined by the profile function. This model permits a calculation of the full multiplicity distribution once the profile function is given. Geometrical scaling and KNO scaling are linked together; the rise in σ_el/σ_tot at the \(Sp\bar pS\) implies a violation of KNO scaling. The energy dependence of moments of the multiplicity distribution is “predicted” quite well. Implications for hard-scattering models are discussed.     

Finding a Probe for Extracting Information on the Momentum Dependent-Interaction in Heavy Ion Collisions

The effect of momentum-dependent interaction on the kinetic energy spectrum of the neutron-proton ratio （ （n/p）gas）b（ Ek ） for 64Zn ＋64Zn is studied. It is found that （ （n/p）gas）b（ Ek ） sensitively depends on the momentumdependent interaction and weakly on the in-medium nucleon-nucleon cross section and symmetry potential. Therefore （ （n/p）gas）b（ Ek ） is a possible probe for extracting information on the momentum-dependent interaction in heavy ion collisions.     

THE INTERACTION OF A HIGH ENERGETIC PROTON WITH A NUCLEUS—THE RELATION OF THE PRODUCED PARTICLES WITH THE NUCLEAR MASS NUMBER A

Suppose that a high energetic proton interacts with a cluster of m particles in anucleus the mean multiplicity of this interaction and that of PP interaction followthe same law: n=CS^k. Using the Glauber theory we get R(A)≡n_PA/n_PP1.26A ^1/3(A ^1/3+1) ^-2/3 This formula explains the current experimental result quite well.     

Is multiple production in proton-proton collisions similar to that ine + e − annihilation?

A model is constructed to simulate recent experimental finding that distributions of hadrons produced in proton-proton collisions are similar to those ine ⁺ e ^? annihilation if the leading proton effects are subtracted properly in the former process. It is found that the predicted multiplicity distribution in proton-proton collisions is too narrow compared to experimental data. As an alternative, we propose a simple quark model that produces correctly the observed multiplicity distribution including the approximate KNO scaling in proton-proton collisions.     

MULTIPLICITY DISTRIBUTIONS OF CHARGED PARTICLES PRODUCED IN pp COLLISIONS AT 400GeV/c

Charged particle multiplicity distributions in pp collisions at 400GeV/c have been studied by using the LEBC films which were offered by CERN NA27 Collaboration.
The corrections to the raw data are described.The results are compared with data at other energies.It is shown that the charged particle multiplicity distribution for the nonsingle diffractive process has KNO scaling behavior,whereas for the inelastic process shows a deviation from KNO scaling up to ISR energy.     

STRATO-GLUON MECHANISM FOR HADRONIC MULTIPLE PRODUCTION AND AVERAGE CHARGED MULTIPLICITY

By assuming that in a high energy hadronic collision process,N pairs of stratonsare produced together with gluons,the number of which is supposed to be propor-tional to the number of“bonds”between any two stratons,we are able to get a rela-tion between the Q-value and the number of pairs N:N=（α²+βQ）^1/2-α.The average charged multiplicity〈n_ch〉_theo is calculated,and is compared withthe experiments.The data of pp、π^±p、K^±p collisions all coincide with the theoreticalcurve in a wide range of energies.The deviation between the energy vs.chargedmultiplicity relations for meson-proton and proton-proton collision processes are ex-plained quantitatively.The average straton mass estimated from the theory is ingood agreement with that.given by other authors.     

Projectile spectator proton production in 84Kr-emulsion interactions at 1.7 A GeV

The multiplicity distribution of projectile protons and multiplicity correlations between black particles, grey particles, shower particles, compound particles, heavily ionized track particles, projectile helium fragments and projectile spectator protons in <'84>Kr-emulsion collisions at 1.7 A GeV are investigated. It is found that the projectile spectator proton multiplicity distribution becomes broader with increasing target mass. The average multiplicity of shower particles and compound particles strongly depends on the number of projectile spectator protons, but the average multiplicity of black particles, grey particles and heavily ionized track particles weakly depends on the number of projectile spectator protons. The average multiplicity of projectile helium fragments increases linearly with increasing numbers of projectile spectator protons. Finally, the multiplicity distribution of projectile spectator protons obeys a KNO type of scaling law.     

A model for multiplicity distributions in hadron-nucleon and α-α interactions at very high energies

We construct a simple stochastic model for particle production in hadron-nucleon collisions, which agrees with experimentally observed KNO scaling. We then use this model to calculate the multiplicity distribution of negative particles produced in α-α collisions at the CERN-ISR, based on a model of multiple collisions. The agreement of the measured spectra with the theory supports this hypothesis.     

Production of Helium Projectile Fragments in 16O-Emulsion Collisions at 60 A GeV

Production of helium projectile fragments in ¹⁶O-emulsion interactions at 60 A GeV is investigated. The total charge changing and partial production cross-sections are measured experimentally on the basis of helium multiplicity. The multiplicity distribution of helium projectile fragments obeys a KNO scaling. In the peripheral collision of ¹⁶O at 60 A GeV in nuclear emulsion, the production of target fragments depends on the multiplicity of helium projectile fragments linearly. The averge multiplicity of target fragments decreases with the increasing of the number of helium projectile fragments which can be well expliained by the model of participant-spectator (the nuclear geometric model) of nucleus-nucleus interactions.     

Multiplicity distributions of produced particles in proton-nucleus collisions at 200 GeV

We analyse data for multiplicity distributions of negative particles which are produced inpp, pAr andpXe collisions, at 200 GeV. We compare two hypotheses with the data: universal (KNO) scaling and the model of independent sources. The data favour the second model.     

A geometrical explanation of multiplicity distributions in relativistic heavy ion collisions

The multiplicity distribution data of NA35 in relativistic heavy ion collisions are fitted based on a geometrical model. The KNO scaling for the same colliding nuclei is obtained. The change of the mean and the shape of the distribution with differentE _veto-andE _T -cuts is also expalined.     

SCALING PHENOMENA AND RENORMALIZATION GROUP

By acting the operator D of the renormalization group equation on the amputa-ted Green's function of N particles,we can deduce the generalized Wroblewski rela-tionship and the corresponding differential equations.Naturally,the Kendall scalingdistribution of the multiplicity is obtained.The scaling variable is proved to be N/〈N〉.Under certain conditions,the inelasticity scaling distribution is also of theKendall type.The parameter of distribution represents relative statistical fluctuationof energy in the central region.     

FINE STRUCTURES OF INCLUSIVE SPECTRA(Ⅰ)——SUM RULES AND THE GENERALIZATION OF FEYNMAN-YANG SCALING

Important implications of the fine structure of inclusive spectra(to be calledinclusive and semi-inclusive spectra of nearby particles,which represent the local dis-tributions of nearby particles in three-dimensional phase space with rapidity y and transverse momenta P_⊥x, P_⊥z as independent coordinates are explained,and some basicfeatures of the fine stucture are found,namely,sum rules and the generalized formof the Feynman-Yang scaling.One of the sum rules,for example,is:where f_(1;k) denotes the normalized invariant inclusive cross section of k closely neigh-boring particles.It follows that the inclusive the spectra of nearby particles arequalitatively different from the usual ones.The generalized form of the Feynman-Yang scaling for the case of k closelyneighboring particles,for example,is:f_(1;k)(s,x₁,P_⊥1,…x_k,P_⊥k⁾∞,（s→∞,x₁≤x₂≤…≤x_k）.where‘∞’denotes‘approaches a definite limit’.For k=2,the existing experimentaldata for the rapidity gap-length distributions show that for FNAL energies,f_(1,k） isalready close to its limiting form.The inclusive（semi-inclusive）spectra of nearbyparticles way be able to reflect effectively short-range correlation effects.     

On the origin of approximate KNO scaling ine + e − annihilation

KNO scaling of the multiplicity distribution in hadronic final states was originally derived as a consequence of Feynman scaling. We show that in iterative models of hadron production in jets, incorporating Feynman scaling, KNO scaling obtains only in the limit when the width of the multiplicity distribution tends to zero. Within the context of the models currently employed to describee ⁺ e ^? annihilation into hadrons, the apparent KNO scaling observed is an accidental consequence of effects which violate Feynman scaling.     

THE COLLECTIVE MOTION OF THE BAG AND THE NUCLEON STRUCTURE FUNCTIONS

Using the hypothesis of the bag-quarks' wave-function with the property of transla-tion invariance, and introducing a Lorentz-invariant effective Lagrangian, we have cal-culated the nucleon deep -inelastic structure functions In our calculation the4-momentum conservation is satisfied automatically, while the resultant structurefunctions are positive-definite and vanish when x>1. Furthermore, using the assumptionof the asymptotic freedom, we obtain explicitly the Bjorken scaling, the approximateexpession F₁ (x～1)∝(1--x)⁴, and by the way, a new counting rule Computercalculation gives the F₂(x) curve which seems to be consistent with the data in therange of 0.4<x<1.     

Geometric scaling,multiplicity distributions and cross sections

From a geometric picture of hadrons as extended objects we arrive at some universal features of high energy collisions. In this approach the mean multiplicity, as a function of s, and the KNO scaling function are universal, and asymptotically the ratio σ_elastic/σ_total is expected to be the same for all processes.     

Characteristics of alpha projectile fragments emission in interaction of nuclei with emulsion

The properties of the relativistic alpha fragments produced in interactions of ⁸⁴Kr at around 1 A GeV in nuclear emulsion are investigated. The experimental results are compared with the similar results obtained from various projectiles with emulsion interactions at different energies. The total, partial nuclear cross-sections and production rates of alpha fragmentation channels in relativistic nucleus-nucleus collisions and their dependence on the mass number and initial energy of the incident projectile nucleus are investigated. The yields of multiple alpha fragments emitted from the interactions of projectile nuclei with the nuclei of light, medium and heavy target groups of emulsion-detector are discussed and they indicate that the projectile-breakup mechanism seems to be free from the target mass number. It is found that the multiplicity distributions of alpha fragments are well described by the Koba-Nielsen-Olesen (KNO) scaling presentation. The mean multiplicities of the freshly produced or newly created charged secondary particles, normally known as shower and secondary particles associated with target in the events where the emission of alpha fragments were accompanied by heavy projectile fragments having Z ≥ 3 seem to be constant as the alpha fragments multiplicity increases, and exhibit a behavior independent of the alpha fragments multiplicity.     

Koba-Nielsen-Olesen scaling

A correct version of Koba-Nielsen-Olesen (KNO) scaling is described in detail for multiplicity distributions. Some statements on the violation of KNO scaling that are based on an erroneous interpretation of experimental data are discussed. An accurate comparison with data is presented for the distributions of negatively charged particles originating from electron-positron annihilation at $\sqrt s = 3 - 161GeV$ , from inelastic proton-proton collisions at p _lab=4.5–520 GeV/c, and from nucleus-nucleus collisions at p _lab=4.5–520 GeV/c per projectile nucleon. Data on proton-antiproton interactions at $\sqrt s = 546GeV$ are also considered.     

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.     

Angular Dependence of Two Particle Correlation in 400GeV/c pp Collisions

The angular dependence of the particle-Particle comeladon (PPC) and its asytiumeby (PPCA) have been calculated by using the experimental data of multiplicity production for pp collisions at 400GeV/ c. The results are different stmngly from the overall behavior of e⁺e^－ data,but agree with the results obtained by NA22 collaboration quite well. The leading particles influence stingily the PPCA disribibudons for hadronic collisions data. The calculated results for the distributions of the azimuthal difference between two pardcles mean that the azimuthal correlation has been observed.