The three-Reggeon vertex: Analyticity, asymptotics and the Toller pole model

Abstract

The incorporation of the local analyticity properties of the six-particle amplitude in a previous treatment of the three-Reggeon vertex is considered. A triple Regge pole contribution is shown to be singular on the boundary between two parts of the physical region where the partial-wave expansion was shown to take different forms. This sungularity can be removed by appropriate behaviour of the residue function, but the asymptotic region where the pole contribution can be expected to dominate behaves unsatisfactorily. For comparison, the connection between the singularity of a Regge pole contribution and the bad behaviour of the asymptotic region is also discussed for the zero momentum transfer problem. Analytic group variables, uniformly related to the invariants are introduced for the six-particle amplitude. A Lorentz-group expansion incorporating the vertex covariance condition is given and a triple Toller pole shown to be a possible uniform asymptotic approximation to the amplitude in the neighbourhood of the boundary considered. The treatment of the three-Reggeon vertex is used to give a full group theoretic treatment of an arbitrary multiparticle amplitude.