Feynman Rules for Regge Particles

Abstract

The analogy between Regge poles and poles due to single-particle exchange is extended to the case of many-particle amplitudes, by considering diagrams with two or more poles. A set of diagrams is obtained in which the internal lines represent Regge particles. The problem of coupling three particles of arbitrary but physical spin is treated first, and coupling constants depending on the helicities are defined. The vertex functions which couple three Regge particles, and which have similar symmetry properties, are defined in terms of the residues of Regge poles. The propagator for a Regge particle with trajectory $\ensuremath{\alpha}(t)$ is essentially a rotation matrix for spin $\ensuremath{\alpha}$, corresponding to a rotation from the initial to the final direction of the center-of-mass momentum, divided by $sin\ensuremath{\pi}(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\sigma})$, where $\ensuremath{\sigma}$ is a constant which replaces the signature. The possibility of using this formalism to predict the high-energy behavior of production amplitudes is discussed, in particular, for single-particle production. As for elastic scattering, one can give a unified description of the low-energy and high-energy regions, and the Regge poles in appropriate crossed channels should dominate in the high-energy region.