Regge Poles in $\pi -\pi$ Scattering

The connection between Regge poles, bound states and resonances, and asymptotic behavior in momentum transfer is reviewed within the framework of the analytically continued $S$ matrix, and a convergent iteration procedure is given for calculating the position and residue of a Regge pole in terms of a given (generalized) potential. By examining the long-range potential in the $\pi \pi$ system, it is inferred that Regge poles should appear in the $I=0\mathrm{}$ and $I=1\mathrm{}$ states, and that the latter pole may be responsible for the $\rho$ meson while the former may well dominate high-energy behavior at low-momentum transfer in the crossed channels. The connection of this possibility with forward coherent (diffraction) scattering in general is explored, and a number of experimental predictions are emphasized. Finally it is shown that the short-range forces due to exchange of 4, 6,... pions are likely to be repulsive and must be included in some form if a consistent solution is to be achieved.