Model for two-pion production in the diffraction approach

Abstract

where e~Ti'(s, t, u) describes the reaction y + P ~ u + r : . They determined T~(s, t, u) by a gauge-invariant kinematical factor and used betafunctions in the invariant amplitudes where a kinematical pole at s = p~ was introduced explicitly. In this paper we give reasons why there is no necessity for introducing the kinematic pole, and we construct a more general model for the reaction V+P-->=+=(V ~ vector particle), modifying an off-shell single-current amplitude in the Veneziano approach proposed in an ear]ier paper (~). We take the point of view here tha t Veneziano 5-point integrals, treating the current as a Reggeon, are the appropriate mathematical functions to descrihe photonic reactions, whereas the beta-functions should only be used to parametrize hadronic reactions. We try to descrihe the above reaction and its hadronic analog p-~P--> T:+r: by making the most simple assumptions such as p-meson exchange in the s-channel and r~-meson exchange in the t and u channels. In Sect. 2 we give reasons why there is no kinematical pole in the helicity amplitudes of the reaction y4-P-->r:+r: -. In Sect. 3 we introduce the invariant expansion of the single-current amplitude and summarize some of the features of the Veneziano 5-point integrals which we will use to descrihe photonic processes. In Sect. 4 we develop the model and discuss its features. Our conclusions are presented in the final Section.