A Model for the Scattering Amplitudes and Its Application to ππ and πN Scattering

概要

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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 amplitudes. 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 ππ amplitudes are constructed in our model under the condition of exchange degeneracy of α_p and α_f. Our model gives good results on scattering lengths. Adler's self-consistency condition gives α_ρ(μ^2)>1/2, which is consistent with the experimental results of α_ρ(0)=0.57±0.01 and is different from Lovelace's results. The high energy amplitudes obey the Gell-Mann mechanism. The πN amplitudes are constructed in our model under the condition of non-exchange degeneracies among α_α,α_δ and α_γ trajectories. Our πN amplitudes satisfy isospin constraints both in low and in high energy regions, and Δα=2. Adler's self-consistency relation is approximately satisfied. The determination of free parameters from low energy resonances predicts high energy amplitudes which are consistent with experimental analysis.
理論物理学刊行会の論文
1970-04-25