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

Abstract

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.