The two-Reggeon/particle coupling

Abstract

A study is made of the two-Reggeon/particle coupling function defined through a production amplitude, with particular reference to its dependence on the Toller angle ω. When one of the Reggeon spins takes a physical value, the coupling function reduces to a polynomial in cos ω. This is understood in several ways: (a) as resulting from the vanishing of non-sense amplitudes in a partial wave decomposition of the production amplitude; (b) in terms of a Fourier transform of the production amplitude; (c) in the perturbation theory; (d) as an extrapolation of the properties of the three-particle coupling that may be deduced from a set of interaction Lagrangians. When the spin of one of the Reggeons in physical the non-vanishing sense amplitudes become equal to the Reggeon/two-particle coupling amplitudes. This is verified in the perturbation theory model for the case of zero spin. The results of the investigation are used to suggest a method of parametrising the two-Reggeon/particle coupling function which allows it to be approximated from a knowledge of ordinary Regge residues. A generalisation of the analysis to the case of parity change at the central vertex is discussed. The implications for non-sense dips in differential cross sections is pointed out. The method of treating external particles with spin is indicated.