J-Plane Structure of the Veneziano Model

The Veneziano model for ${\pi }^{+}{\pi }^{-}$ elastic scattering is subjected to $J$-plane anaylsis, and it is shown in that in the finite $J$ plane it consists only of Regge poles and fixed poles at nonsense wrong-signature points. The residues of the leading and first two subsidiary trajectories are computed explicitly, and an algorithm is derived for the computation of all others. In deriving the algorithm, the Mandelstam form of the Reggepole series is obtained. It is shown that this series is asympotic in a certain domain, but not convergent, thus demonstrating the essential role of the background integration in producing crossing symmetry. The relation between the Veneziano residues and those of the Khuri model is discussed, as well as some other features of the $J$-plane structure.