Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 1

Abstract

We demonstrate a possibility of computation of inelastic scattering cross-section in a multi-peripheral model by application of the Laplace method to multidimensional integral over the domain of physical process. Founded the constrained maximum point of scattering cross-section integral under condition of the energy-momentum conservation. The integrand is substituted for an expression of Gaussian type in the neighborhood of this point. It made possible to compute this integral numerically. The paper has two parts. The hunting procedure of the constrained maximum point is considered and the properties of this maximum point are discussed in the given part of the paper. It is shown that virtuality of all internal lines of the “comb” diagram reduced at the constrained maximum point with energy growth. In the second part of the paper we give some the arguments in favor of consideration of the mechanism of virtuality reduction as the mechanism of the total hadron scattering cross-section growth, which is not taken into account within the framework of Regge theory

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

“…Using the Laplace's method we have found [1,2] the mechanism of partial cross-section growth, which was not taken into account in the previously known variants of multi-peripheral model. This mechanism may be responsible for the experimentally observed increase of hadronhadron total cross-section.…”

“…As shown in [1], each term in sum shown in Figure 1 with accuracy up to the fixed factor is a function with real and positive values, which has a constrained maximum if its arguments satisfy the mass-shell conditions and energy-momentum conservation law. Therefore, in the c.m.s.…”

“…Therefore, in the c.m.s. of initial particles function corresponding to the left-hand part of cut diagram in Figure 2 can be rewritten in the neighborhood of maximum point in the form [1,2].…”

“…However, as it was shown in [1] near the threshold of the particles production at the maximum point of the n n. Where , ˆj ( ) P k , k = 1, 2,  n denote the number into which a number k goes due to permutation…”

“…This paper is the sequel to [1,2], where to calculate protonproton scattering partial cross-sections within the framework of multi-peripheral model the Laplace method was applied.…”