Singularity of the Elastic Scattering Amplitude of Hadrons at Small Impact Parameters

Abstract

On the basis of the fact that the amplitude of elastic pp scattering is well described in the high energy region by the contribution of a dipole pomeron and an odderon, the profile function is calculated in this approximation and its behavior is investigated in the region of small impact parameters. It is shown that the profile function in this region does not have any singularities, and they arise only in the limit of small phase volumes (i.e., as the Planck constant tends to zero ħ → 0). The behavior of the elastic cross section and of $ \left\langle {{b^2}} \right\rangle $ as s → ∞ is investigated. It is shown that these characteristics increase as the logarithm of the energy ratio $ ln\frac{s}{{{s_0}}} $ .