On the role of longitudinal momenta in high energy hadron-hadron scattering

We demonstrate a new method to calculate inelastic scattering cross-sections, which in contrary to the Regge-based methods takes into account the energy momentum conservation law. It is shown that the main contribution to integral expressing inelastic scattering cross-sections does not come from the multi-Regge domain. In particular, accounting for the longitudinal momenta contribution to virtualities is sufficient and results in the new mechanism of cross-section growth. The reasons for taking into account the sufficiently high number of interference contributions are shown and the approximate method for this purpose is developed. By fitting single free parameter of the model achieved a qualitative agreement of the total and inelastic cross sections with experimental data.