Compositeness, Feynman Diagrams, and the Reggeized Absorption Model

In this paper we derive the Reggeized absorption model from field-theoretic diagrams. This model has been used to describe a large number of quasi-two-body reactions. It involves a Regge-cut correction to Regge-pole amplitude which is generated by the exchange of the Regge pole and a Pomeranchuk pole. The cut features the product of the Reggeon and Pomeranchon (without complex conjugation of either) and a large magnitude for the cut (coherent inelastic effects add to the original cut term). The fundamental physical assumption of our derivation is that physical particles are composite objects of constituent pieces of matter. In a scattering process, some of the constituent matter takes part in the scattering while the rest stands by as a spectator. These ideas lead us to describe double-scattering processes by a class of diagrams involving exchange of two Reggeons in the crossed channel and propagation of composite physical particles in the direct channel. When the direct-channel particles are Reggeized, we obtain an expression for the Regge box diagram. We begin our analysis of diagrams by discussing the Amati-Fubini-Stanghellini diagram and similar diagrams to demonstrate how the absence of third double-spectral functions leads to the absence of a cut. For simple diagrams, we find that we are forced to invoke properties of form factors to show absence of the cut, but that for sufficiently composite diagrams the absence of the cut rests solely on the absence of the third double-spectral functions. Next we discuss the Mandelstam diagram and similar diagrams to demonstrate how the presence of third double-spectral functions leads to cuts. For each diagram we bring the expression for the amplitude to the form of the absorption model. Finally, we study the general class of diagrams referred to above. These diagrams feature compositeness in the direct channel (physical particles are composite), third double-spectral functions (physical particles have definite signature; no exchange degeneracy), and two-Reggeon exchange (double scattering and the Glauber spectator approximation). By assuming saturation of direct-channel amplitudes by physical states, we are led to an absorption formula (no complex conjugations) that includes the coherent inelastic factor λ (diffraction production of direct-channel resonances).