Cumulative Phenomena through the Quark-Parton Diagram Summation at   Thresholds
  A microscopic treatment of cumulative phenomena based on perturbative QCD calculations of the corresponding quark diagrams near the threshold is presented. To sum all diagrams like these the special technique based on the recurrence relations was developed. The x-behaviour of the nuclear structure function $F_{2}(x)$ in the cumulative region x>1 was found to be roughly exponential, governed by an effective coupling constant, which depends on the QCD coupling constant and quark mass. Two mechanisms for cumulative particle production, direct and spectator ones, were analysed. It was shown that due to final state interactions the leading terms of the direct mechanism contribution are cancelled and the spectator mechanism is the dominant one. It leads to a smaller slope of the particle production rates compared to the slope of the nuclear structure function in the cumulative region, in agreement with the recent experimental data. The slope difference is due to additional multiple interactions between nuclear and projectile partons which enter the spectator mechanism for the cumulative production. The different versions of hadronization mechanisms of the produced cumulative quarks into hadrons are also discussed. 
M.A. Braun and V.V. Vechernin (St.Petersburg State University)