Veneziano Representation with the Pomeranchuk Trajectory

A term containing the Pomeranchuk trajectory is constructed for the Veneziano representation of the $\pi \pi$ scattering amplitudes. It contributes to direct-channel resonances (recurrences of $P$) only in the $I=0\mathrm{}$ amplitude and gives proper asymptotic behavior for all isospin amplitudes. Taking the same slope as the $\rho$ trajectory and normalizing to the asymptotic cross section of 15 mb, we obtain an $I=0\mathrm{}$, $J=2\mathrm{}$ resonance at 1 BeV with a width of 75 MeV. The Adler condition is satisfied, and the contribution of the Pomeranchuk term to the scattering lengths is very small.