Self-Reproducing Conditions on the Pomeranchuk Singularity
Haruo Fujisaki · Progress of Theoretical Physics · 1970
A “self-reproducing" bootstrap model is proposed for the Pomeranchukon, by the use of a Reggeization procedure of production amplitudes by Gribov, Pomeranchuk and Ter-Martirosyan. On the basis of the analysis of two Pomeranchukon contribution to the crossed-channel unitarity, it is shown that, in order to satisfy the “self-reproducing” condition, the Pomeranchukon must be a fixed branch point or two colliding branch points, with the intercept equal to 1. It is also argued that the discontinuity across the Pomeranchukon will not be determined by the unitarity alone. On the assumption of a standard form of the discontinuity, our model predicts two typical features of the diffraction scattering in the asymptotic energy region. First, the total cross sections decrease faster than 1/log s and s tends to infinity. Secondly, the ratio of real to imaginary parts of the forward amplitude is negative and decreases like 1/log s at large s. These predictions are irrespective of whether the Pomeranchukon is fixed or moving.