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

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 φ 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 s with a characteristic minimum in the range s ≈ 10 GeV. However, quantitative agreement was not achieved; we assume that due to the fact that we have examined the simplest diagrams of 3  theory.

New method of accounting for interference contributions within a multiperipheral model

“…Let us substitute the expression (10) for the scattering amplitude T n ð ffiffi ffi s p ; XÞ in the expression of the partial cross section (12):…”

“…At the same time, it is possible to specify, without any assumptions, the integration domain which makes a main contribution to the multidimensional integrals for the scattering cross section. It has been shown (see [9][10][11][12][13][14]) that the squared modulus of the multiperipheral diagram contribution to the scattering amplitude has quite a distinct conditional maximum given that the energy-momentum law is satisfied. This maximum point may be found either using any numerical method or analytically within a certain approximation [10].…”

“…An absence of the strong ordering of rapidities makes it pointless to consider the multiperipheral diagrams without considering the interference contributions (which represent the various ways of joining of the identical particle lines to the diagram [9,12]). Although the values of the interference contributions may be small, their number is too large to be neglected.…”

“…Although the values of the interference contributions may be small, their number is too large to be neglected. Moreover, it has been shown (see [12]) that the contribution from the ladder diagram is much smaller compared to the sum of the other contributions. Each interference contribution can be calculated quite easily with Laplace's method [9][10][11][12][13][14] even for the large number of secondary particles n. However, it is problematic to account for the large number of such contributions even for numerical computations.…”

“…Moreover, it has been shown (see [12]) that the contribution from the ladder diagram is much smaller compared to the sum of the other contributions. Each interference contribution can be calculated quite easily with Laplace's method [9][10][11][12][13][14] even for the large number of secondary particles n. However, it is problematic to account for the large number of such contributions even for numerical computations. Therefore, the objective of this work is to propose an approximate calculation method which would allow one to calculate the sum of all the interference contributions for the processes with a large number of secondary particles (n ∼ 50).…”