Gluon propagator in classical color field of colliding hadrons and its implications for hadronic cross sections

We review the Regge theory and the minijet model for pp and pp collisions. We show that, in the conventional minijet approach, the asymptotic behavior of the total cross section calculated using currently accepted gluon distribution function and perturbative QCD rises too rapidly when compared with the data and fails to satisfy Froissart bound. To tame the rise, we have developed a new formalism for the interaction between QCD gluon and the classical color field of the colliding nucleons, and show how the gluon propagator is modified. The corresponding gauge invariance condition of the propagator is derived and shown to be satisfied. The modified gluon propagator leads to a suppression of the minijet cross section due to the gg [rightwards arrow] gg sub-process in the small-x region. We show that the pp and pp total cross section from [square root]s = 5 GeV to 30 TeV can be described as a sum of a hard component contributed by the classical field modified minijet model and a soft component due to the exchange of the Pomeron and the I=0 exchange-degenerate [omega] and f Regge trajectories. The soft-component model is motivated by the notion of duality. The predicted total cross section has a ln s asymptotic behavior.