Z. Koba

SCALING OF MULTIPLICITY DISTRIBUTIONS IN HIGH ENERGY HADRON COLLISIONS.

Abstract It is shown that asymptotically 〈 n 〉 σ n ( s ) is only a function of n /〈 n 〉, where σ n ( s ) is the multiplicity distribution. The essential assumption in deriving this result is that multiparticle inclusive cross sections obey the scaling law. It is also pointed out that the available data below 30 GeV may possibly indicate rather long-range correlations in multi-body reactions.

Reaction amplitude for n-mesons a generalization of the Veneziano-Bardakçi-Ruegg-Virasoro model

Abstract The Veneziano model for the binary meson reaction ( n = 4), generalized by Bardakci and Ruegg and by Virasoro to n = 5, is further extended to the case of arbitrary n . The multi-resonance structure of the n -meson reaction is analyzed with the help of “quark diagrams”. An integral representation for the reaction amplitude, its basic properties (recurrence formulae, multi-poles and multi-Reggeization) are presented. A consistent normalization leads to certain relations between coupling constants and trajectory slopes.

Manifestly crossing invariant parametrization of n meson amplitude

Abstract Utilizing the geometric property (of being certain anharmonic ratios) of the variables u , which are ‘conjugate’ to the Regge trajectories in the generalized Veneziano amplitude for the n -meson reaction, an integral representation of the latter is constructed in such a way that all the external mesons appear on an equal footing and thus all the requirements of crossing symmetry are fulfilled. A precise mathematical meaning can be ascribed to our integral representation.

CROSS-CHANNEL ISOSPIN ANALYSIS OF PERIPHERAL SINGLE-PION PRODUCTION PROCESSES.

Abstract A cross-channel isospin analysis of experimental data on peripheral single-pion or single-rho-meson production processes will lead to evaluation of the I = 0 and I = 1 exchange amplitudes, if the I ≥2 exchange is absent.

Scaling in semi-inclusive experiments

Abstract In bubble chamber experiments (in contrast to counter experiments) the semi-inclusive experiment a+b→c+(n−1) charged + anything neutral is more natural than the corresponding inclusive experiment a+b→c+anything. We argue that the cross sections for semi-inclusive experiments have very neat scaling properties.

GENERATING FUNCTIONALS FOR MULTIPLE PARTICLE PRODUCTION: SEMI-INCLUSIVE CROSS SECTIONS, MOMENTUM DISTRIBUTIONS, AND CORRELATIONS.

Abstract A generating functional formalism for multiple production in high-energy hadron collisions is developed. It includes, as two special cases, Predazzi-Venezianos formula and Muellers generating function. It summarized in a concise way the kinematical relations among exclusive, semi-inclusive, and inclusive cross sections, single- and multiple-particle momentum distribution and correlation functions, their partial and total integrals, as well as the energy-momentum sum rules. A few simple cases and the asymptotic limit, which reveals the scaling behaviour, are treated in this framework. The following important equivalence theorem is shown: the information contained in the set of all inclusive many-particle cross sections is equivalent to the information contained in the set of all exclusive many-body cross sections.

Structure of overlap function and peripherality of production processes

Abstract Contributions of inelastic channel wave functions in the momentum representation to the elastic diffraction constant are analysed, using the overlap function method, and are interpreted on the basis of the wave-packet formalism. The elastic diffraction constant is shown to consist of a sum of two positive terms coming form the modulus and the phase of inelastic channel wave functions, respectively. The uncorrelated-jet model and the multi-Regge model are investigated in detail.

Generalized Veneziano model from the point of view of manifestly crossing-invariant parametrization

The construction of the Veneziano-typen-point function with manifestly crossing-invariant parametrization is reviewed in a heuristic way. Here, one meets a divergence problem, the solution of which is discussed in detail. Equivalence to previous works and its asymptotic behaviour are rederived with the help of affine group representation.

Isospin analysis of hadronic production processes at high energy

Abstract Consequences of isospin invariance are discussed under usual circumstances of hadronic production processes at high energy; one has to do with a large number (typically three or more) of isospin amplitudes and analyze cross sections which are averaged and summed with respect to helicities and integrated over a certain region of phase space. After such summation and integration the constraints (due to relative phases of the isospin amplitudes), which relate differential cross sections, are lost; but, intead, we get weaker constraints in the form of inequalities. General forms of these inequalities and their implications are presented. They are often useful in evaluating upper and lower limits of integrated isospin amplitudes when the number of available charge channels is not sufficient for determining the latter. Examples are given for single-pion production processes with emphasis on the estimation of various isospin exchange mechanisms, in particular that of I = 0 exchange. We illustrate the method by using experimental data from KN → K π N at 3 GeV/ c .

ISOSPIN ANALYSIS OF PION AND NUCLEON RESONANCE PRODUCTION IN NN COLLISIONS.

Abstract After a brief survey of isospin relations for the general reaction NN→N′N′ + kπ ( k = 1, 2, 3, …), cases of k = 2, 3 and resonance formation are discussed. The reaction NN → N′ Δπ is found particularly suitable for the isospin analysis, and its cross sections are given in terms of various isospin exchange amplitudes. Another eventually feasible example is NN → N′ Δϱ .