Regge Poles and Resonances in Strong Interaction

The scattering of two particles via the exchange of a resonance system is considered. The exchanged resonance is approximated by a pole in the Regge representation. The composite nature of the resonance is taken into account in the Regge-pole description so that one does not encounter divergence difficulties even though the exchanged resonance may be in a $J=1$ state.The exchange of a ππ ($I=1$, $J=1$) resonance in pion-pion scattering is considered in some detail. It is shown that this exchange mechanism produces a strong attractive force in the $I=1$ scattering system. Whether this exchange force can reproduce a resonance at the observed energy depends on a dimensionless parameter in the representation. This dimensionless parameter is restricted to be positive and of order unity on the basis of a crude uncertainty-principle argument. The value of the parameter required to reproduce a resonance does fall within this range. However, the width of the calculated resonance is broader than the observed width by a factor of 2 to 3. This discrepancy is not unexpected since all other forces in the problem have not been considered.