A theorem on high-energy scattering amplitudes

Abstract

A theorem is presented which allows, starting from amplitudes with well-defined high-energy behaviour, to construct a new amplitude, which turns out to be asymptotically larger than the original ones. Application to amplitudes represented by certain classes of any kind of graphs (e.g. A3theory or multiperipheral graphs) leads to a statement on the actual high-energy scattering amplitudeT. If it has a high-energy behaviour of the form\(f \cdot 8^a \left( {\log {\text{ }}s} \right)^\beta \left( {\log _2 {\text{ }}s} \right)^{\gamma _{2...} } \left( {\log _n {\text{ }}s} \right)^{\gamma _2 } \) the class of graphs corresponding toT must include generalized ladder diagrams which contain every 2-particle irreducible graph with 4 external lines an infinite number of times as generalized rungs.