High-energy Inelastic Processes Research Articles

Isobaric-gas model for high-energy nuclear physics

We develop a model for high-energy inelastic processes. The model is primarily intended for collisions of nuclei, however the equilibrium conditions permit its application also to hadron-hadron collisions. The model is constructed on a hydrodynamical basis and takes into account nuclear shock waves. Pionization is obtained in an indirect way (production of isobaric resonances which subsequently decay or annihilate themselves). The nuclear temperature as a function of «s» is obtained and a comparison with experiment is made. Also an expression for the multiplicity is obtained. Hadron matter density may become during the collision many times greater than the normal nuclear density.

Clusters and the rapidity interval method

An effective method of analysing the experimental jets with the aim of discovering the clusterization phenomenon of particles produced in high-energy inelastic processes is proposed. The method exploits the set of all possible rapidity intervals,i.e. rapidity differences of two particlesyi+k+1 −yi with somek particles having rapidities in between (the usual gap corresponds tok = 0). It provides information which is in principle as complete as that obtained from the correlation functions. It is simple in application and physically clear. The method is applied to various models and the rapidity interval distributions thus obtained are compared to the experimental data for π−p 40 GeV and pp 70 and 200 GeV collisions. The important role of clusterization of secondary particles follows from this comparison. It is predicted that the two-bump structure should develop fork ≥ 4 and large multiplicities in pp interactions at 200 GeV if two baryonic clusters were produced.

Direct-simulation Monte Carlo models for high-energy inelastic processes

Three Monte Carlo models are presented for providing descriptions of center-of-mass angular distributions, longitudinal and transverse momentum distributions, and effective-mass distributions for multiparticle final states produced in high-energy inelastic processes. They are applied specifically to the reaction pp → ppπ+π−, and the results are compared with experimental data for this reaction at incident-proton laboratory momenta of 22 GeV/c and 10 GeV/c. One of the models I involves a virtual dissociation of the target (projectile) into pπ+π− with projectile (target) involved only to the extent that its longitudinal momentum is reduced sufficiently to permit the target (projectile) associated pπ+π− to be freed in the final state with overall energy-momentum conservation. A second model II has the target (projectile) dissociating into pπ+ and the projectile (target) dissociating into pπ−. Both I and II include additional exchanged systems to provide transverse-momentum transfer from the target to projectile system. The last model III is based on a virtual dissociation of both target and projectile into a proton and another system (mass taken as zero). These two systems combine and decay into π+ and π−. It is shown that a particular combination of I and III provides a good qualitative description of the ppπ+π− data at both 10 GeV/c and 22 GeV/c.

Bootstrap Model for Diffractive Processes: Complementarity of the Yang and Regge Models

The Yang (or droplet) model and the Regge model for high-energy diffractive processes are contrasted, their complementarity emphasized. The combination of the physical aspect of the former with the mathematical aspect of the latter gives rise to a bootstrap model which has far-reaching consequences. The assumptions of the bootstrap model are: (a) High-energy inelastic processes are dominated by the two-cluster diffractive fragmentations; (b) the $s$ dependences of diffractive scattering and fragmentation are the same; and (c) partial-wave amplitudes can be continued uniquely into the complex $j$ plane. We study the boot-strap of the Pomeranchon in both the $s$ and the $t$ channel using inelastic unitarity without approximation. The Pomeranchuk singularity is found to be a branch point with $\ensuremath{\alpha}(0)=1$ exactly; discontinuity of the associated cut vanishes at the tip. Both forward and nonforward cases are considered. Various properties of diffractive scattering and fragmentation at high energy are obtained. On the basis of the bootstrap model, we make predictions on (1) the asymptotic behavior of ${\ensuremath{\sigma}}_{\mathrm{tot}}$, (2) the ratio of real to imaginary parts of scattering amplitude, (3) the absence of physical manifestation of the Pomeranchon, (4) the dependence of fragmentation cross section on the effective masses of the particle clusters, (5) the average multiplicity of hadron production, (6) the diffraction peak of fragmentation process, and (7) the relationship between $\mathrm{pp}$ and $\ensuremath{\gamma}p$ diffraction peaks. All of these predictions are consistent with whatever relevant data are available at present. If, in addition, a technical assumption is made concerning the Reggeization of production amplitudes, the precise nature of the Pomeranchuk branch point can be determined.

A dynamical scheme for leading trajectory and theory of fireballs

The quantum-field theory based on the Bethe-Salpeter equation is applied to investigate properties of the leading vacuum trajectory for the elastic amplitude and to describe high-energy inelastic processes. It is shown that it naturally explains the production of fireballs at very high energies. Parameters of the leading trajectory are related to characteristics of inelastic processes.

A model for high-energy inelastic processes

A model for high-energy inelastic processes

Possible Existence of a Spin-2 Regge Recurrence of theS01 p−pPole (The Unbound Diproton)

A model is developed wherein the $^{1}D_{2}p\ensuremath{-}p$ partial-wave amplitude is coupled through $\frac{N}{D}$ equations to a second, inelastic channel containing a proton and a second particle in a relative $S$ wave. The mass of the second particle is smeared out according to an appropriate Breit-Wigner form around the (3,3) resonance at $1260\ensuremath{-}i120$ MeV. The phenomenological potential is adjusted to fit the elastic $^{1}D_{2}$ phase shift to 400 MeV and the existing imprecise data at 660 MeV. The model, when adjusted to fit experiment, predicts a pole on the second Riemann sheet at $400\ensuremath{-}i300$ MeV. This pole may be interpreted as a bound state in the inelastic channel and has quantum numbers ($I=1$, $B=2$, $J=2$) consistent with the spin-2 Regge recurrence of the pole in the $^{1}S_{0}$ amplitude, the unbound diproton. An alternative coupled-channel model is developed which fits the elastic data but which does not predict the pole. The high-energy predictions for elastic scattering which are derived from the second model are found to differ drastically from those of the first model and from the predictions of various theories for high-energy inelastic processes.

A model for high-energy inelastic processes

The problem of expressing the high-energy inelastic amplitudes in terms of the elastic amplitudes that couple through unitarity is discussed. A solution to this problem is given by approximately solving the unitarity equations with assumptions similar to the ones usually made in the absorptive model, together with a high-energy factorization property. The surprising result is obtained that the inelastic amplitudes are completely expressible in terms ofall the elastic ones that have the correct quantum numbers to couple through unitarity. Some general properties of this solution are investigated for π−p and K−p charge exchange by using an exact Fourier-Bessel representation which is derived by means of techniques previously developed. Similarly to what happens in the Byers and Yang droplet model, the high-energy inelastic amplitudes in the forward direction show an exponentially decreasing peak (as function of the momentum transfer), if this is present in at least one of the elastic (initial and final) channels. The question of whether the forward peak of the inelastic amplitude is narrower or wider or comparable to the elastic one is seen to require a very detailed parametrization of the elastic data. In principle, in our model, there are no arbitrary parameters left since the inelastic amplitudes are completely determined from the knowledge ofall the elastic ones. In practice, however, the limitation of experimental information at our disposal forces us to introduce an empirical energy-dependent factor. Within the framework of our model, little can be said about this energy-dependent factor. If, however, one makes the extra assumption that all the elastic channels are comparably equal and that the number of channels open at a given (high) energy have the same energy dependence as the multiplicity, then it can be seen that very good agrement is obtained, in this approximation, for π−→π0n which is the only case for which a sufficiently large statistics exists. No detailed numerical comparison of the theory with experimental data is attempted in this preliminary paper.

Is absorption necessary in high-energy inelastic processes?

We present two arguments against the presence of important absorptive effects in high-energy physics. The first comes from the phenomenological analysis of single-pion production in pp collisions and the second from the application of the random phase approximation to the unitarity condition for an inelastic process.

Diffraction scattering in the multiperipheral model

Evidence that only part, not all, of the elastic scattering amplitude for diffraction scattering in the multiperipheral model displays Regge pole behavior is noted. For high energy inelastic processes, only the part of the elastic amplitude due to intermediate inelastic states displays such behavior. A way to evaluate the complete diffraction scattering that is the shadow of the inelastic absorption given by the model is proposed. (D.C.W.)

Strong damping of large momentum transfers, and its consequences for high-energy inelastic processes

High-energy inelastic processes are treated in a model which resembles the repeated one-pion exchange model, but with the (t - μ2-1 dependence of pion exchange on momentum transfert replaced by a decreasing exponential dependence. The exponential dependence is motivated by, and assumed to be similar to, elastic proton-proton scattering results. The fireball emerges as a natural concept in this model, and results in qualitative agreement with many properties of cosmic-ray interactions are obtained. The model does not involve Regge poles explicitly, but some problems connected with Regge poles in inelastic processes are discussed in an Appendix.