Mixing of Regge Poles and Cuts in a Field-Theory Model

Abstract

The Regge poles generated by ladder diagrams in a λ φ³ theory are mixed with the moving cuts generated by a class of nonplanar graphs containing an internal ladder. Since the contribution from the cut‐generating diagram is of order t⁻²ln ^mt, where t is the asymptotic variable, the t⁻² behavior of the pure ladder graphs is examined and the trajectory of the Regge pole near $\ell$ = −2 is calculated. The Mellin transform method is used throughout. The transformed amplitude corresponding to a single cut insertion is given by a product of the form pole‐cut‐pole, where it is only the second Regge trajectory that mixes with the cut. The cut itself depends on the leading trajectory. This result substantiates the predictions as to form of other work based on unitarity, but differs in that the cut and pole depend on different trajectory functions. Finally, multiple insertions of the cut diagrams are shown to generate an amplitude with two moving poles on each sheet of the cut.