Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 2

What is it about?

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 < 8) number of secondary particles in within the framework of phi3 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.

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Why is it important?

From demonstrated results it can be conclude that replacing of the "true" scattering amplitude associated to the multi-peripheral processes within the framework of perturbation theory by its Gaussian approximation is an acceptable approximation. The main conclusion is, that the mechanism of virtuality reduction may play a major role in ensuring the experimentally observed increase of the total cross-section, at least in some range of energies. This growth was obtained with allowance for sigma_n at n<8. However, as it follows from sigma_n'(sqrt(s)) dependencies, the maximum point of cross-section is shifted toward to higher energies with increase of n. We can therefore expect that in the consider energy range accounting of sigma_n'(sqrt(s)) will add summands with positive derivative with respect to energy to expression for the total scattering cross-section, which leads to the fact that at least in the considered energy range obtained growth will only intensify. The application of Laplace method is not limited by simplest diagrams. Therefore, our goal is further consideration of the more realistic models using same method, especially in terms of the law of conservation of electric charge.