Self-Reproducing Pomeron and Diffraction Scattering

Abstract

In a previous paper ,ll we have discussed a self-reproducing model of the Pomeron, on the basis of the postulate that the effect of multi-Pomeron exchange is exactly the same as that of single-Pomeron exchange as far as type and position of the singularities are concerned. Our model automatically satisfies the maximum strength hypothesis and yields the trajectory function of the Pomeron free from any threshold singularities. In fact, the solution is a fixed branch point a (t) = 1, or a pair of colliding branch points a± (t) = 1 ± r vt, with r being a real, non­ zero parameter. 2 > In our bootstrap model, however, the discontinuity across the Pomeranchuk branch cut cannot be uniquely determined. In this note, we m­ vestigate the asymptotic behaviour of diffraction scattering by the use of the self-reproducing Pomeron with a general form of discontinuity. We confine ourselves to the scattering of spinless, identical particles, and consider the four-body amplitude F(s, t) normalized as 16n