ModifiedπNSuperconvergence and the Static Model

Abstract

Recently, superconvergence relations have been proposed for certain scattering amplitudes with spin at fixed momentum transfer. Unfortunately, the kinematics and high-energy behavior of $\ensuremath{\pi}N$ scattering do not permit any such relations for this process. If, however, one assumes Regge-pole dominance at high energy, one can write superconvergence relations for certain amplitudes from which the leading Regge-pole contributions have been subtracted out. Assuming resonance dominance in the low-energy region, one has a sum rule relating these resonances to the Regge parameters. Comparison with experimental data in the forward direction shows that the Regge contribution is small and that the dominant resonances are the $N$ and ${N}^{*}$; the sum rule is then approximately satisfied. Completely ignoring the Regge poles and making certain additional assumptions leads to a relativistic version of the static model, which gives a relation, for instance, between the $N$ and ${N}^{*}$ coupling constants. This relation is quite well satisfied. In addition one may derive the Adler PCAC (partially conserved axial-vector current) self-consistency condition. These results are shown to be related to the vanishing of the equal-time commutator of the pion currents.