Self-Reproducing Flat Pomeron in the Eikonal Approximation

Abstract

where ac (t) is the trajectory function of the branch point of the cut in the complex angular momentum plane, non-zero r with ac (t) = 1 ± r v't corresponds to a pair of colliding Regge cuts and vanishing r to a fixed cut at J = 1. However, in Fujisaki's model the property of the discontinuity of the cut is not determined uniquely so that the asymptotic behavior of the contribution from the self-reproducing Pomeranchuk cut is indefinite as far as the logarithmic dependence on energy is concerned. In this paper it is shown that in the framework of eikonal approximation a flat pomeron (a(t) =1) of simple pole type (no logarithmic factor in the asymptotic behavior) is a unique solution of the selfreproducing condition provided that the Pomeranchuk trajectory is linear. We consider the elastic scattering of equal mass spinless particles. We assume that the contribution from primordial pomeron to the amplitude is given by