A Model for the Scattering Amplitudes and Its Application to π π and πNScattering

Abstract

A new model for scattering amplitudes is proposed. This model satisfies the finite energy sum rule, unitarity at threshold, and other desirable physical properties of scattering ampli­ tudes. In this model daughters are also contained and the duality in our sense is related to Regge pole and cut (scattering state) duality, which is different from the conventional duality relating only to Regge poles. The rcrc amplitudes are constructed in our model under the condition of exchange degen­ eracy of aP and af. Our model gives good results on scattering lengths. Adler's self-con­ sistency condition gives aP (p.2) >l, which is consistent with the experimental results of ap (0) =0.57±0.01 and is different from Lovelace's results. The high energy amplitudes obey the Gell-Mann mechanism. The rcN amplitudes are constructed in our model under the condition of non-exchange degeneracies among aw a~ and a 7 trajectories. Our rcN amplitudes satisfy isospin constraints both in low and in high energy regions, and L1a=2. Adler's self-consistency relation is ap­ proximately satisfied. The determination of free parameters from low energy resonances predicts high energy amplitudes which are consistent with experimental analysis.