Model of the Pomeranchuk Pole-Cut Relationship

Abstract

Using the multiperipheral integral equation at zero momentum transfer, we construct a model in which the dynamical interrelation of Regge poles and cuts can be studied. Chief attention is paid to the region near $J=1\mathrm{}$ in an elastic forward amplitude. A consistent solution is found in which the Pomeranchuk pole appears at $J=1-a$, with $a\gtrsim 0.01$, while the Amati-Fubini-Stanghellini (AFS) branch point appears at $J=1-2a$. To a good approximation, the pole residue corresponds to the inelastic part of the total cross section, while the integral over the AFS cut corresponds to the elastic cross section.