We describe a QCD motivated model for total cross-sections which uses the eikonal representation and incorporates QCD mini-jets to drive the rise with energy of the cross-section, while the impact parameter distribution is obtained through the Fourier transform of the transverse momentum distribution of soft gluons emitted in the parton-parton interactions giving rise to mini-jets in the final state. A singular but integral expression for the running coupling constant in the infrared region is part of this model.
@article{arxiv.0810.3411,
title = {Zero momentum gluons and the total pp and pbarp cross-sections},
author = {A. Achilli and R. M. Godbole and A. Grau and G. Pancheri and Y. N. Srivastava},
journal= {arXiv preprint arXiv:0810.3411},
year = {2008}
}