Alternative Constructions of Crossing-Symmetric Amplitudes with Regge Behavior

Abstract

A representation for the scattering amplitude that contains Regge behavior, crossing symmetry, and analyticity is discussed. It is shown that it provides a different ghost-eliminating mechanism (the Mandelstam-Wang one) from that given by Veneziano's proposal. Furthermore, it does not restrict the external masses, but reduces to Veneziano's formula when $\alpha \mathrm{}\left(s\right)+\alpha \mathrm{}\left(t\right)+\alpha \mathrm{}\left(u\right)\mathrm{}$ equals a particular integer that depends on the reaction. Several examples are discussed. The behavior of the Regge residue ${\beta }_{\rho \pi \pi }\mathrm{}\left(t\right)\mathrm{}$ at ${\alpha }_{\rho }\mathrm{}\left(t\right)=0\mathrm{}$ is proposed as a test that distinguishes the two representations.