On the parton picture of Froissart asymptotic behavior

Abstract

The Froissart (\F) asymptotic behavior of high energy cross-sections, if considered in a parton picture, is usually represented as a kind of behavior that occurs in the process of a collision of two almost black disks, filled with partons, when radiuses of these \F - disks grow proportional to log's of there energies. In this article we briefly summarize the main asymptotic properties of \F - disks that one can expect in QCD. ~~Then we consider if it is possible to guarantee the boost-invariance of transparency $T(s,b) = 1 - \sigma_{in}(s,b)$, where $\sigma_{in}(s,b)$ is the total inelastic cross-section at a definite impact parameter $b$, in process of collision of two such \F-disks. Such a question arise because the mean transverse area of the overlapping of colliding \F- disks, at the same impact parameter b and total energy $\sqrt{s}$~,~ is varying with the Lorentz frame. ~~We show that the value of $T(s,b)$ is not boost-invariant at some $b$ close to the \F- disk border for the \F- disks usually expected in QCD. As result the \F type behavior seems contradictory, or the multiparton system in the high energy Fock wave function must be arranged in rather unusual way.