On the role of longitudinal momenta in high energy hadron-hadron   scattering
  We demonstrate a new method for the calculation of inelastic scattering cross-section, which in contrary to the Regge-based methods takes into account the energy momentum conservation law. By virtue of this method it was shown that the main contribution to integral expressing inelastic scattering cross-sections comes not from the multi-Regge domain. In particular this leads to the fact that accounting of longitudinal momenta contribution to virtualities is sufficient and results in the new mechanism of cross-section growth. The necessity of taking into account the large number of interference contributions is shown and the approximate method for this purpose is developed. By considering the interference contributions from a single fitting constant achieved a qualitative agreement of the total and inelastic cross sections with experimental data. 
Igor Sharf, Andrii Tykhonov, Grygorii Sokhrannyi, Maksym Deliyergiyev,   Natalia Podolyan, Vitaliy Rusov
hep-ph