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Hadronic Total Cross-sections Through Soft Gluon Summation in Impact Parameter Space

The Bloch-Nordsieck model for the parton distribution of hadrons in impact parameter space, constructed using soft gluon summation, is investigated in detail. Its dependence upon the infrared structure of the strong coupling constant $α_s$ is discussed, both for finite as well as singular, but integrable, $α_s$. The formalism is applied to the prediction of total proton-proton and proton-antiproton cross-sections, where screening, due to soft gluon emission from the initial valence quarks, becomes evident.