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

## TL;DR

This paper introduces a novel method to account for interference effects in proton-proton inelastic cross-sections within a multi-peripheral model, revealing significant contributions outside traditional multi-Regge domains and aligning qualitatively with experimental energy dependence.

## Contribution

It develops a new approach to include interference contributions in the multi-peripheral model using Laplace's method, challenging the assumption that multi-Regge domains dominate the integrals.

## Key findings

- Interference contributions are significant and not limited to multi-Regge domains.
- The model qualitatively reproduces the energy dependence of total cross-section.
- Approximate integration allows calculation of partial cross sections for many secondary particles.

## Abstract

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 Laplace's 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.