Soft QCD dynamics of elastic scattering in the 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: gluon clouds of valence quarks with size $\sim 0.3\hspace{0.5em}\mathrm{fm}$ and hadronic size $\sim 1\hspace{0.5em}\mathrm{fm}.$ The presence of the two scales unavoidably leads to a specific form for the total hadronic cross section which consists of a steeply rising $\propto s^{\Delta }\hspace{0.5em}(\Delta =0.17\mathrm{}\pm 0.01)$ 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. To further test the model, we analyze the elastic $\mathrm{pp}$ and $\overline{p}p$ 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 1 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.