Unitarization of Total Cross Section and Coherent Effect in pQCD

I want to discuss a method to unitarize the leading-log BFKL Pomeron [1], so that the growth of total cross section σT (s) with energy √ s obeys the Froissart bound ln s. The idea is very simple. Total cross section grows because the Yukawa cloud of the colliding particles overlap even at large impact parameters. At low energy the clouds are so tenuous and transparent that they do not contribute to the cross section. But as energy increases, the rarified overlap may contain sufficient energy to produce there a gluon jet, or a pair. When that happens the cloud becomes opague and the effective radii inrease. This continues until shadowing correction becomes important, at which time the rise is dampened and the Froissart bound is reached. This idea is familiar with potential scattering, where Born approximation, if large, must be supplemented by higher-order corrections to restore unitarity. In the present context, instead of potentials we must talk about interacting Reggeons, but the idea is the same. The technical question is how to do so in QCD, where the basic entities are quarks and gluons carrying non-commuting colours, rather than Reggeons. Clearly a characterization of multiple Reggeons in terms of quarks and gluons are needed. We shall show that this can be derived with the help of an s-channel factorization property, which also leads to an eikonal form for the amplitude which includes shadowing correction needed for the Froissart bound to be obeyed. Moreover, such a factorization is almost synonomous to the statement that the state in the peripheral region in the collision is coherent.