Introduction

Having identified, in the previous chapter, some of the leading Regge trajectories from the resonance spectrum, we next want to look more closely at the other main aspect of Regge theory, the way in which Regge poles in the crossed t channel control the high energy behaviour of scattering amplitudes in the direct s channel.

For spinless-particle scattering this presents few problems; we would simply use the expression (2.8.10) in the region where t is small and negative, and s is large. However, for real experiments with spinning particles it is a bit more difficult because, as we shall find in the next section, the t-channel helicity amplitudes contain various kinematical factors, and are subject to various constraints, which must also be incorporated in the Regge residues. Also we shall need to look closely at the behaviour of the residue function when a trajectory passes through the nonsense points discussed in section 4.5. Only when we have clarified these kinematical requirements can we write down correct expressions for the Regge pole contribution to a scattering amplitude based on (4.6.15).

In exploring these kinematical problems we shall discover that some of the difficulties at t = 0 may imply the occurrence of additional trajectories called ‘daughters’ and ‘conspirators’, and we shall briefly review the application of group theoretical techniques to such problems. Also we examine the way in which the internal SU(2) and SU(3) symmetries constrain Regge pole exchange models.