Two-fireball Model Research Articles

Hadron–hadron interactions at high energy via Rademacher functions

Charged particles multiplicity distributions for hadron–hadron interactions at high energy have been studied. Two cases are considered: the proton–proton (p–p) and the pion–proton (π–p) interactions. The parton two-fireball model based on an impact parameter is adopted. The overlapping functions, known to be complicated and nonlinear, are approximated employing a series of Rademacher functions. The analysis has been facilitated, since Rademacher functions are linear, analytic and mathematically simple. The accuracy of the approximation is tunable through the order of the employed Rademacher functions. Theoretical expressions for inelastic cross-sections and the charged multiplicity distributions have been derived employing the proposed representation. Figures are provided to demonstrate good agreement between theoretical calculations and experimental data at different energies. Formulae for the change of some important parameters with the variation of high energy have been derived employing least square curve fitting techniques.

Multiplicity distribution of heavy particles for hadron–nucleus interactions

In this work we apply an impact parameter analysis depending on the parton–two-fireball model (PTFM) to study the high-energy interactions of hadrons with nuclei. In this model, hadrons are considered as bundles of point-like particles (partons). Total cross-sections for proton–nucleus and pion–nucleus interactions at high energies have been calculated and compared with observations. Different parameters controlling multiparticle production of heavy particles have been calculated and compared with the corresponding experimental data.

Two-fireball model for hadron production in lepton-hadron scattering

A two-fireball model for hadron production, related to the model developed in Phys. Rev. D 20, 1093 (1979), reproduces the average charged-secondary-hadron multiplicity and the disperson $D={(〈{n}^{2}〉\ensuremath{-}{〈n〉}^{2})}^{\frac{1}{2}}$ observed in deep-inelastic neutrino-proton scattering.

Approximate method of including finite particle number effects in relativistic heavy ion collisions

We show that for large momenta the grand canonical ensemble is not an accurate enough approximation to the phase space integral to be used in calculating inclusive cross sections. In its place we propose a very general method based on the saddle point inversion of the Laplace transform integral. This method is shown to be quite accurate and is used to calculate deuteron inclusive spectra in conjunction with a two-fireball model.

Improvements to the two-fireball model for relativistic light ion collisions

A revised version of the two-fireball model for relativistic light ion collisions is presented. This version utilizes our knowledge from nucleon-nucleon or nucleon-nucleus collisions to give an essentially parameter free transparency formulation. Calculations are done for proton and pion spectra.NUCLEAR REACTIONS Relativistic collisions of ions; fireball; proton and pion spectra.

C12onC12at 800 MeV/Nucleon: One Fireball or Two?

I demonstrate that a two-fireball model can explain the proton and pion inclusive spectra for collision between light ions at relativistic energies. For havier ions, the one-fireball model is recovered.

Two-fireball model of e +e − -annihilation into hadrons at high energies and the jet problem

Two-fireball model is proposed to describe the e +e −-annihilation into hadrons. The jet problem and the scaling are discussed. The results obtained for one-particle inclusive distribution and some other characteristics are in quite good agreement with experimental data.

Rich Yield of High Momentum Hadrons by Two-Fireball Model in eFormula Annihilation

Rich Yield of High Momentum Hadrons by Two-Fireball Model in eFormula Annihilation

Analysis of multiple-production phenomena on the basis of niu’s two-fireball model

Analysis of multiple-production phenomena on the basis of niu’s two-fireball model

Internal Multiplicity Distributions of Geometric Models

In geometric models of high-energy collisions, it is of great physical interest to find out what are the internal multiplicity distributions at a given impact parameter. We derive formulas connecting these distributions with measurable quantities for a wide class of models, thereby hoping to gain insight into the internal compositions of hadrons once sufficient experimental data become available. The application of these formulas is illustrated in the text with a two-fireball model, and models without internal number fluctuations.

Inclusive spectra in single- and double-excitation models

The inclusive pion spectra in p-p collisions predicted by the single-excitation (or Nova) model and the double-excitation model are discussed. The description is given in terms of the rapidityy, which facilitates the comparison of the two models. Whereas in the limit of infinite energies the two models may be shown to have the same form, their predictions at accelerator and even at ISR energies differ appreciably. In particular we discuss the question of how the scaling limit in the central region is reached, and which factors in the model govern the approach. The problem of enforcing a cut-off in momentum transfer is examined, and it is found that the effect of such a cut-off is to cause a dip in the central plateau. However the effect is much more severe for the double-excitation model than for the single-excitation one. Furthermore the contribution of the two-fireball model to the inelastic cross-section is found to increase considerably between accelerator and ISR energies, to such an extent that it should be the dominant process at very high energies.

Double-Peakedlogtan12θDistributions and Their Relation to Fireballs

The double-peaked feature of the $logtan\frac{1}{2}\ensuremath{\theta}$ distribution of secondary particles in a cosmicray jet is predicted not only by the two-fireball model, but also by a number of other phenomenological and empirical models. It is shown that in these models there is also a simple explanation for the occurrence of the two peaks, namely, the independence of ${p}_{\ensuremath{\parallel}}$ from ${p}_{t}$ in the c.m. system. Infinite-fireball models do not lead to the double-peaked distribution even when two groups (or clouds) of fireballs are considered.

Momentum Spectrum of Hadronic Secondaries in the Multiperipheral Model

Motivated by a simplified multiperipheral model, we formulate a general qualitative description of the momentum spectrum of secondaries, resulting from a collision of two hadrons at high energies. Arguing from two fundamental multiperipheral concepts, (a) that transverse momenta are limited and (b) that distant particles on the multiperipheral chain are uncorrelated, we predict that at sufficiently high incident energies, the momentum spectrum of particle $X$ in the reaction $a+b\ensuremath{\rightarrow}X$+anything, when presented in the variables ${p}_{\ensuremath{\perp}}$ and $y=invsin[\frac{{p}_{\ensuremath{\parallel}}}{{({{p}_{\ensuremath{\perp}}}^{2}+{m}_{{X}^{2}})}^{\frac{1}{2}}}]$, develops a central plateau in the $y$ dependence, which elongates and flattens to a value that is normalized by the total cross section as the incident energy increases. Moreover, it is shown that the resultant particle density distribution is consistent with the hypothesis of limiting fragmentation. We contrast this description with the predictions of the two-fireball model, the isobar-pionization model, and the statistical thermodynamical model.

Two-Fireball Phenomenon and the Multiperipheral Model

In the context of the Chew-Snider version of the Amati-Bertocchi-Fubini-Stanghellini-Tonin pion-exchange model, we investigate certain multiperipheral mechanisms that could account for those phenomena that have hitherto motivated the two-fireball model. These mechanisms are (1) double diffractive dissociation, (2) the presence of a sequence of neutral particles on the multiperipheral chain, and (3) statistical fluctuations in the $\mathrm{logtan}\ensuremath{\theta}$ spectrum. At cosmic-ray energies they are of equal importance.

A semi-statistical model of high-energy collisions

The emission of particles directly created in high-energy collisions is considered to be only partly governed by statistical laws as in Fermi's model. The motion of the created particles is to some degree related to the former motion of the incoming colliding particles. In first approximation this intermediate state is built up of two extremes: two Lorentz systems are introduced from which the particles are emitted isotropically and according to statistical laws. In the centre-of-momentum system (CMS) of the collision these two systems move in the directions of the incoming particles after collision. This approximation corresponds to the two-fireball model which we regard as a representative of a mathematical method of dealing with correlations. In further approximation phase space distributions are replaced by the thermodynamic Fermi or Bose distributions for relativistic particles. Both experimental data such as the nearly constant mean transverse momentum¯pt and phase space calculations with constant interaction volume show that the temperaturekT reaches an upper limit asymptotically at high energies; the asymptotic region begins at about 30 GeV. The comparison with experimental particle spectra from accelerators in the 10–30GeV region shows good agreement if one uses a smooth dependence ofkT on the collision energyE0 and, for each independent set of measurements, an individual choice of\(\bar \gamma _f \), the mean Lorentz factor of the “fireballs” in the CMS, and of ¯n, the mean number of created particles. The pt-distribution of pions and the dependence of¯pt on the particle mass can also be successfully described. At very high energies the model gives production ratios of the various kinds of particles which lie within the range of the experimental determinations. The dependence of\(\bar \gamma _f \) onE0 is concluded to be of the form\(\bar \gamma _f \propto E_0^{1/2} /\bar n(E_0 ) \approx 0.5E_0^{1/4} \), i.e. CMS anisotropy is related to multiplicity.

Three-dimensional simulation of air showers. Core structures

Three-dimensional Monte Carlo simulations of extensive air showers were made with a model of nuclear interaction based essentially on the two-fireball model. Monte Carlo simulations were tried with primary protons of energy 106 and 2.5 × 105 GeV. Various quantities related to electrons, nuclear-active particles, and muons were obtained which enable us to get detailed information on the development of individual showers.Among various features so far simulated, those of core structures, in particular, are presented in great detail and discussed in connection with shower development. Within the framework of the fireball model the following main features were noted for the formation of multiple electron cores. The fraction of multicored events is strongly dependent on the primary energy, and decreases considerably with increasing height. These events were all initiated at high altitudes and none of them had high-density peaks with a separation of a few or more meters. High-energy nuclear particles play an important role in producing multicored events, but none of the peaks in multi-cored events were produced by a single γ ray.These features, in comparison with the experimental results, require the introduction of a large mean transverse momentum for nucleons, particularly at high energies [Formula: see text]. It seems likely that it increases with energy.

Nucleon-Nucleon Interactions at Energies Greater than1012ev

A primary jet of type $2+16p$ and a high-energy secondary jet of the same type as that of the primary, i.e., $2+16p$, were observed in nuclear emulsion. A very high energy electromagnetic cascade was also observed in the primary interaction. Both the primary and the secondary interactions were considered as nucleon-nucleon for their analysis. The energy as calculated from the angular distribution of the shower particles of the primary and of the secondary events is 3.1\ifmmode\times\else\texttimes\fi{}${10}^{12}$ and 2.5\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ev, respectively. The estimate of the energy of the primary event is also obtained from its total energy dissipated. The validity of the energies of the primary as well as of the secondary events as obtained from their angular distribution is discussed. The average transverse momentum of the shower particles is \ensuremath{\sim}0.30 Bev/c. The energy and the angles of shower particles of both these events are transferred to the c.m. system which shows sharp collimation of particles of high energy at small angles with the shower axis. The energy distribution in the c.m. system for both these events is peaked towards low values but shows a remarkably long tail at high energies extending up to 12 Bev. Analysis of both these events is consistent with the two-fireball model.