Veneziano Amplitude: Interference Models and Argand Loops

In the Veneziano model, at large $s$ and fixed $t$, the $s$-channel resonances sum to give $\Gamma (1-\alpha \mathrm{}(t\left)\right){\mathrm{}(-s)\mathrm{}}^{\alpha \mathrm{}\left(t\right)-1\mathrm{}}$ and the $u$-channel resonances sum to $\Gamma (1-\alpha \mathrm{}(t\left)\right)s^{\alpha \mathrm{}\left(t\right)-1\mathrm{}}$. Using this feature, we propose a new interference model for intermediate energies which gives a significantly improved fit to the backward ${\pi }^{-}p$ data, and we make comments on the Schmid Argand loops.