High-Energy Elastic and Inelastic Scattering inϕ3Theory

We study high-energy elastic and inelastic processes in a ${\varphi }^3$ theory based on the following model: For the elastic-scattering amplitude we first sum the leading terms in each order of perturbation of the $t$-channel straight ladders, plus those obtained by interchange of the Mandelstam variables $s$ and $u$. We then perform the $s$-channel iteration with the $t$-channel ladders as single units. We are only interested in the physical regions in which the incident particles retain their large momenta. This procedure leads to the eikonalization of the $t$-channel ladders. For the inelastic production amplitude, the dominant contribution comes from diagrams with any number of totally open ladders (i.e., multiperipheral chains) modified by unopen ones. The main results are: (a) The total cross section approaches zero, approaches a constant, or increases as ${\left(\mathrm{lns}\right)}^2$ according as the coupling constant is smaller than, equal to, or larger than a critical value. (b) Elastic and inelastic differential cross sections are computed, and they have many nice features, as suggested by the absorption model. (c) Nonforward $s$-channel unitarity is explicitly verified. (d) One-particle and multiparticle spectra, the average multiplicity, the number distribution of the final particles, etc., are obtained. The implications of these results to hadron physics are discussed.