Soft gluon resummation in the infrared region and the Froissart bound

Abstract: We describe the taming effect induced by soft gluon $k_t$-resummation on the rapid rise of QCD mini-jet contributions to the total cross-sections.This results from an eikonal model in which the rise of the total cross-section is due to mini-jet contribution. We perform the calculation with current Parton Density Functions (PDFs). The impact parameter distribution we use is obtained as the Fourier transform of the resummed $k_t$-distribution of soft gluons emitted from the initial state during the collision.The emission, which is energy dependent, destroys the initial collinearity of partons.In this model, the strong power-like rise due to the increasing number of low-x gluon collisions is tamed by the acollinearity induced by soft gluon kt-resummation down to zero gluon momenta. It explicitly links a singular soft gluon coupling in the infrared region to the behaviour dictated by the Froissart bound for the total cross-section. The model describes well both proton and photon processes at present accelerator energies and gives predictions in the TeV range. For photons the model predictions agree with fits by Block and Halzen based on Finite Energy Sum Rules (FESR) at low energy and an asymptotic behaviour consistent with the Froissart bound.