Mechanisms of proton-proton inelastic cross-section growth in multi-peripheral model within the framework of perturbation theory. Part 2

We demonstrate a new technique for calculating proton-proton inelastic cross-section, which allows one by application of the Laplace method replace the integrand in the integral for the scattering amplitude in the vicinity of the maximum point by expression of Gaussian type. This in turn, allows one to overcome the computational difficulties for the calculation of the integrals expressing the cross section to sufficiently large numbers of particles. We have managed to overcome these problems in calculating the proton-proton inelastic cross-section for production (n le 8) number of secondary particles in within the framework of phi^3 model. As the result the obtained dependence of inelastic cross-section and total scattering cross-section on the energy sqrt{s} are qualitative agrees with the experimental data. Such description of total cross-section behavior differs considerably from existing now description, where reggeons exchange with the intercept greater than unity is considered.

Mechanisms of proton-proton inelastic cross-section growth in multi-peripheral model within the framework of perturbation theory. Part 3

We develop a new method for taking into account the interference contributions to proton-proton inelastic cross-section within the framework of the simplest multi-peripheral model based on the self-interacting scalar phi^3 field theory, using Laplaces method for calculation of each interference contribution. We do not know any works that adopted the interference contributions for inelastic processes. This is due to the generally adopted assumption that the main contribution to the integrals expressing the cross section makes multi-Regge domains with its characteristic strong ordering of secondary particles by rapidity. However, in this work, we find what kind of space domains makes a major contribution to the integral and these space domains are not multi-Regge. We demonstrated that because these interference contributions are significant, so they cannot be limited by a small part of them. With the help of the approximate replacement the sum of a huge number of these contributions by the integral were calculated partial cross sections for such numbers of secondary particles for which direct calculation would be impossible. The offered model qualitative agrees with experimental dependence of total scattering cross-section on energy {sqrt s} with a characteristic minimum in the range {sqrt s approx 10} GeV. However, quantitative agreement was not achieved; we assume that due to the fact that we have examined the simplest diagrams of phi^3 theory.