Soft QCD Dynamics of Elastic Scattering in Impact Parameter   Representation
  The elastic hadronic amplitude is calculated using the nonperturbative light-cone dipole representation for gluon bremsstrahlung. The data for large mass diffraction demand a two-scale structure of light hadrons: the gluon clouds of the valence quarks with a size of 0.3fm and the hadronic size 1fm. The presence of the two scales unavoidably leads to a specific form for the total hadronic cross section which consists of a steeply rising \propto s^{\Delta} (\Delta=0.17 +/- 0.01) term related to gluon radiation, and a large constant term originating from soft interactions which does not induce any gluon emission. Our calculations reproduce well the total cross sections and elastic slopes \cite{k3p}. To further test the model, we analyze the elastic pp and ppbar differential cross sections and extract the partial amplitudes in the impact parameter representation. The Pomeron trajectory as a function of the impact parameter is only slightly above one for central collisions, but steeply grows towards the periphery. The model predicts correctly the shape and energy dependence of the partial amplitude at all impact parameters. 
B.Z. Kopeliovich, I.K. Potashnikova, B. Povh and E. Predazzi