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 $\ensuremath{\alpha}(s)+\ensuremath{\alpha}(t)+\ensuremath{\alpha}(u)$ equals a particular integer that depends on the reaction. Several examples are discussed. The behavior of the Regge residue ${\ensuremath{\beta}}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}(t)$ at ${\ensuremath{\alpha}}_{\ensuremath{\rho}}(t)=0$ is proposed as a test that distinguishes the two representations.