Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 3

What is it about?

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 phi3 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 demonstrate that since 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) ~10 GeV. However, quantitative agreement was not achieved; we assume that due to the fact that we have examined the simplest diagrams of phi3 theory.

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Why is it important?

From obtained result, one might conclude that the considered mechanism of virtuality reduction at the constrained maximum point of multi-peripheral scattering amplitude may be responsible for proton-proton total cross-section growth when all the considerable interference contributions are taken into account. Just the revelation of mechanism of cross-section growth we consider as the main result of earlier papers and present work, since this mechanism is intrinsic not only to the diagrams of the "comb" type, but also to different modifications of considered model. Application the Laplace method allow to calculate another types of diagrams corresponding to various scenarios of hadron-hadron inelastic scattering and compare it with experimental data.