Partial Bootstrap of the Schizophrenic Pomeranchon

Abstract

The Pomeranchuk ($P$) trajectory and residue near $t=0\mathrm{}$ are calculated through self-consistency requirements from properties of the $P^{\prime }$. The calculation is based on a general multiperipheral model whose kernel is assumed to be nonsingular near $J=1\mathrm{}$, $t=0\mathrm{}$, apart from a small component associated with Pomeranchon exchange and containing the corresponding Amati-Fubini-Stanghellini (AFS) branch point. This small component of the kernel is treated by standard perturbation techniques. The self-consistent $P$ trajectory turns out to have a slope smaller than normal and substantial positive curvature, whereas the logarithmic derivative of the residue is abnormally large. Although these effects result from proximity to the AFS branch point in the multiperipheral kernel, the corresponding branch point in the amplitude itself turns out to be relatively unimportant near $t=0\mathrm{}$.