Statistical hadronization model and transverse momentum spectra of hadrons in high energy collisions

A detailed analysis of transverse momentum spectra of several identified hadrons in high energy collisions within the canonical framework of the statistical model of hadronization is performed. The study of particle momentum spectra requires an extension of the statistical model formalism used to handle particle multiplicities, which is described in detail starting from a microcanonical treatment of single hadronizing clusters. Also, a new treatment of extra strangeness suppression is presented which is based on the enforcement of fixed numbers of pairs in the primary hadrons. The considered center-of-mass energies range from to 30 GeV in hadronic collisions ( and Kp) and from 15 to 35 GeV in collisions. The effect of the decay chain following hadron generation is accurately and exhaustively taken into account by a newly proposed numerical method. The exact conservation at low energy and the increasing hard parton emission at high energy bound the validity of the presently taken approach within a limited center-of-mass energy range. However, within this region, a clear consistency is found between the temperature parameter extracted from the present analysis and that obtained from fits to average hadron multiplicities in the same collision systems. This finding indicates that in the hadronization process the production of different particle species and their momentum spectra are two closely related phenomena governed by one parameter. Received: 31 October 2001 / Published online: 15 February 2002     

Transverse momentum and transverse mass distributions of charged hadrons produced in Au--Au collisions at high energies

The transverse momentum distribution and the transverse mass distribution of charged hadrons produced in nucleus nucleus collisions at high energies are described by using a two-cylinder model. The results calculated by the model are compared and found to be in agreement with the experimental data of the STAR and E895 Collaborations, measured in A~Au collisions at the relativistic heavy ion collider （RHIC） and alternating-gradient synchrotron （AGS） energies, respectively. In the energy range concerned, the excitation degree of emission source close to the central axis of cylinders increases obviously with the collision centrality and incident energy increasing, but it does not show any obvious change with the increase of the （pseudo）rapidity in central collisions. The excitation degree of emission source close to the side-surface of cylinders does not show any obvious change with the collision centrality, the （pseudo）rapidity, and the incident energy increasing.     

Transverse momentum spectrum of mesons produced in high energy nucleus-nucleus collisions

The momentum of all charged mesons produced in 19 high energy, high multiplicity nucleus-nucleus collisions of cosmic rays in emulsion have been measured. The transverse momentum distribution differs qualitatively from proton-proton collisions at comparable energies. One possible interpretation is in terms of a transverse explosion with effective temperature T=78 MeV and transverse flow velocity υ=0.61c.     

Transverse momentum of charged hadrons observed in deep inelastic muon scattering

The transverse momenta of charged hadrons produced in high energy muon-proton scattering have been studied. The average squared transverse momentum 〈p²_⊥〉 shows a strong dependence on z = E_h/v characteristic of intrinsic momentum effects and a significant rise as a function of s = W². The W², q², x and z dependences of the data are compared with the predictions of a perturbative QCD model.     

Transverse momentum distributions of hadrons produced in αα and αp collisions at the CERN intersecting storage rings

The inclusive production of charged hadrons has been measured in αα and αp collisions at nucleon-nucleon c.m. energies (√s_nn)of 31 and 44 GeV, respectively, for transverse momenta p_T up to 5 GeV/c in the central rapidity (y) region. at high p_T the yields are consistent with being 4 times and 16 times highere than the ones in pp interactions at y=0, for αp and αα interactions, respectively. However, an enhancement over these factors, as expected from an earlier FNAL experiment, cannot be ruled out.     

Transverse-momentum spectra of hadrons produced in central heavy-ion collisions

In-medium effects of transverse-mass distributions of quarks and gluons are considered assuming a possible local equilibrium for colorless quark objects like mesons and baryons created in central AA collisions. It is shown that the average square of the transverse momentum for these partons grows and then saturates when the initial energy increases. Within the quark-gluon string model, it leads to an energy dependence of hadron transverse-mass spectra which is similar to that observed in heavy-ion collisions. A comparison with other scenarios is given. The text was submitted by the authors in English.     

Multiplicity distributions of charged hadrons at AGS, SPS and RHIC

It is found that Collective Flow Model (CFM) which can successfully analyze charged particle distributions at AGS and lower SPS (less than 20 GeV/n), fails to analyze that of RHIC. The tail of distribution of charged particle at RHIC has a jump away from the collective model calculation as the energy increase. Thermalization Component Model (TCM) is presented basing on collective flow to study the multiplicity distributions at RHIC in this paper. It is realized that the limitation of phase space of collective flow can denote that of thermalization region. By comparing the contributions of particle productions from thermalization region at different energies and different centrality, we can deep our study on the feature of collective movement at RHIC.     

Azimuthal correlation and fractal study of compound hadrons (pions and protons) at Dubna and SPS energy

This paper presents an investigation of compound hadrons (pions and protons) distribution emitted from ²⁴Mg-AgBr and ¹²C-AgBr interactions both at 4.5 AGeV and ³²S-AgBr interactions at 200 AGeV. The study includes azimuthal correlations (two particle and three particle), azimuthal asymmetry and fractal behaviour. This paper reveals some interesting results.     

Transverse spectra of waves in random media

Abstract

We consider the statistics of the transverse spectra of forward-propagating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the long-range evolution of the ensemble-averaged transverse wave spectrum and coherence. The conditions under which these equations may be approximated by differential and integro-differential equations are given, and it is shown that the approximation is valid for the treatment of beam propagation provided that the transverse dimension of the beam is sufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenable to numerical solution by marching techniques. We use the equation that governs the spectral density of the total energy flux, and also the propagation of waves which are statistically homogeneous in transverse planes, to show the conditions under which previously studied approximations derive from the present formulation, and to illustrate the numerical solution of the problem.     

Transverse momentum of muon pairs produced in hadronic collisions

The observed p_⊥ distributions of large mass muon pairs produced in proton-nucleus collisions are quantitatively explained in QCD by also explicitly taking into account the intrinsic wave function p_⊥ spread of partons inside the hadrons. The experimental data indicate 〈p_⊥〉 ～ 500–600MeV for each parton.     

Transverse spectra of waves in random media

We consider the statistics of the transverse spectra of forward-propagating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the long-range evolution of the ensemble-averaged transverse wave spectrum and coherence. The conditions under which these equations may be approximated by differential and integro-differential equations are given, and it is shown that the approximation is valid for the treatment of beam propagation provided that the transverse dimension of the beam is sufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenable to numerical solution by marching techniques. We use the equation that governs the spectral density of the total energy flux, and also the propagation of waves which are statistically homogeneous in transverse planes, to show the conditions under which previously studied approximations derive from the present formulation, and to illustrate the numerical solution of the problem.     

Open charm contribution to dilepton spectra produced in nuclear collisions at SPS energies

Measurements of open charm hadro-production from CERN and Fermilab experiments are reviewed, with particular emphasis on the absolute cross sections and on their A and √s dependences. Differentialp _T andx _F cross sections calculated with thePythia event generator are found to be in reasonable agreement with recent data. The calculations are scaled to nucleus-nucleus collisions and the expected lepton pair yield is deduced. The charm contribution to the low mass dilepton continuum observed by the CERES experiment is found to be negligible. In particular, it is shown that the observed low mass dilepton excess in S-Au collisions cannot be explained by charm enhancement.     

Heisenberg model and a random walk on the permutation group

It is shown that the isotropic Heisenberg model can be analysed in terms of a random walk on the permutation group. This approach makes it intuitively clear why the Heisenberg model exhibits long range order or ferrogmagnetic behavior in three dimensions and not in two and one dimensions. This approach to the Heisenberg model lends itself to computer analysis.Work supported in part by the National Science Foundation     

Transverse momentum distribution of the Z produced at the Large Hadron Collider and related phenomena

From the recent theoretical result on the production of the Higgs boson at the Large Hadron Collider, it follows that other particles will also be produced with small transverse momentum, of the order of 1 GeV/c$1\text{GeV}/c$. The leptonic decay mode of the Z is especially suited for a first observation of this phenomenon. Other related effects, such as paired jets, are also discussed.     

Free energy and some sample path properties of a random walk with random potential

We study the asymptotic behavior of the free energy for a model (defined by Sinai) of one-dimensional random walk with random potential. In particular, we obtain a central limit theorem and a strong law of large numbers for this free energy. We use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization. Some exponents describing the recurrence and localization are found.     

On the transverse momentum distribution of strange hadrons produced in relativistic heavy ion collisions

Particles with strange quark content produced in the system 1.93A·GeV⁵⁸Ni on⁵⁸Ni have been investigated at GSI Darmstadt with the FOPI detector system. The correlation of these produced particles was analyzed with respect to the reaction plane. baryons exhibit a very pronounced sideward flow pattern which is qualitatively similar to the proton flow. However, the kaon (K ⁺,K _s ⁰ ) flow patterns are significantly different from that of the protons, and their form may be useful to restrict theoretical models on the form of the kaon potential in the nuclear medium.The authors would like to thank G. Q. Li for helpful correspondence.     

Simplicity of “transverse energy” spectra of hadrons

Using data from a 16 GeV/cπ⁺p bubble chamber experiment, we have studied the production of pions and meson resonances in the central region. Transverse spectra have been analysed in terms of the transverse energy variable E_t=√p_t²+M². We find that the E_t spectra of “stable” particles, of resonances like ?, ω and f, and of corresponding non-resonant two- and three-pion systems all follow one simple exponential in E_t over several orders of magnitude in cross section. All spectra are consistent with one common slope parameter of approximately (120 MeV)^?1.     

Transverse momentum bounds and scaling in the hydrodynamical model

It is shown that the equation of state of an ideal relativistic gas, as applied in the hydrodynamical model, leads not only to deviations from scaling in longitudinal rapidity distributions, but also to an average transverse momentum increasing asymptotically as a power of the incident energy. To prevent such an increase, one must use the equation of state of an interacting gas, in which the velocity of sound becomes asymptotically equal to that of light. This then also restores scaling (up to logarithmic terms) in longitudinal rapidity.     

Transverse momentum spectra in high-energy nucleus-nucleus, proton-nucleus and proton-proton collisions

The transverse momentum distributions of final-state particles produced in nucleus-nucleus (AA), proton-nucleus (pA), and proton-proton (pp) collisions at high energies are investigated using a multisource ideal gas model. Our calculated results show that the contribution of hard emission can be neglected in the study of transverse momentum spectra of charged pions and kaons produced in Cu-Cu collisions at √s_NN=22.5 GeV. And if we consider the contribution of hard emission, the transverse momentum spectra of p and p produced in Cu-Cu collisions at √s_NN=22.5 GeV, K_s⁰ produced in Pb-Pb collisions at 158 A GeV, J/ψ particles produced in p-Pb collisions at 400 GeV and π⁺ , K⁺, p produced in proton-proton collisions at √s=200 GeV, can be described by the model, especially in the tail part of spectra.     

Coherent backscattering and localization in a self-attracting random walk model

Intensity propagation of waves in dilute 2D and 3D disordered systems is well described by a random walk path-model. In strongly scattering media, however, this model is not quite correct because of interference effects like coherent backscattering. In this letter, coherent backscattering is taken into account by a modified, self-attracting random walk. Straightforward simulations of this model essentially reproduce the results of current theories on “non-classical” transport behavior, i.e. Anderson localization in 1D and 2D for any amount of disorder and a phase transition from weak to strong localization in 3D. However, in the strongly scattering regime corrections are necessary to account for the finite number of light modes due to their non-vanishing lateral extention. Within our model this correction leads to the observation that strong localization does not take place. Received 17 September 2001