Regge trajectory structure of the Amati-Bertocchi-Fubini-Stanghellini-Tonin multiperipheral model

Abstract

The Regge pole spectrum of the ABFST multiperipheral model with a resonance kernel is studied, using both the forward and nonforward partial-wave integral equations. Insight into the complicated pattern of the trajectory spectrum is provided by an analysis of the singularity structure of the basic kernel using appropriate representations for it, and by an elucidation of the process of generation of trajectories in the weak-coupling limit. This also establishes a framework for understanding the characteristics of the approximate solutions to the problem that are taken up subsequently. The trace approximations for both the nonforward and forward equations are worked out in detail. The traces involved are evaluated in convenient closed forms from which all the necessary information can be extracted easily. It is found that the approximation preserves, to a fair degree of accuracy, the trajectory-generating singularity structures of the relevant kernels, and that good `effective' trajectory positions for the leading and secondary poles are obtained in both the forward and nonforward cases. It is also shown that, in this approximation, other phenomena such as complex Regge poles, the threshold behavior of the trajectories, and the intercept and slope of the leading trajectory can be investigated in a close simulation of the actual situation. Recent factorizable approximations are then examined from the point of view of the pole spectra they lead to, and it is concluded that, by and large, they oversimplify the problem and that their shortcomings are thus more extensive than those of the trace approximation.