Abstract
Abstract Elastic and total cross-sections are discussed using an eikonal formalism in the QCD framework. For this purpose, we construct analytic and integrable αs(S) consistent with confinement. It is applied with success in obtaining the intrinsic transverse momentum and towards an improved description of τ decay. Analyticity is imposed to obtain bounds on the impact parameter distribution. A hadronic string picture is employed to find relationships between the intercepts and slopes of the Pomeron and other leading Regge trajectories. The above are combined with a Bloch-Norsieck summation of soft gluons to tame an otherwise too fast a rise of the cross-sections.
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