Complex-l-Plane Singularities in the Veneziano Formula

The continued partial-wave projection of the Veneziano formula is performed and the complex-$l$-plane singularities are investigated. It is explicitly shown that in the $\pi \pi$ amplitudes given by the Veneziano-Lovelace model there are an infinite series of Regge poles with parallel trajectories spaced by one unit and an essential singularity as $\mathrm{Re}l\to -\infty$, For the even-signature amplitude, besides the singularities mentioned above, additive fixed poles are shown to be present at nonsense wrong-signature points. The classification of the Regge-pole family in terms of Lorentz poles and the positivity condition for the Regge-pole residues are also discussed.