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

TL;DR

This paper introduces a new Gaussian-based technique within perturbation theory to compute proton-proton inelastic cross-sections for up to eight secondary particles, aligning qualitatively with experimental data.

Contribution

It presents a novel Laplace method-based approach to overcome computational challenges in calculating multi-particle inelastic cross-sections within the ^3 model.

Findings

The method successfully calculates cross-sections for up to 8 particles.

Results qualitatively match experimental energy dependence.

The approach differs from reggeon exchange models.

Abstract

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.