Abstract
We consider the forward π-π dispersion relations for T = 0 and T = 2 in a soluble model. The model is based on two assumptions. (i) The π-π cross section has the same constant asymptotic value for all isobaric states (Pomeranchuk theorem). (ii) The forward amplitude becomes pure imaginary at infinite energies. For simplicity we only consider cases with one or no CDD poles in each isobaric state. We find two solutions which are consistent with the constraints of crossing: Solution A has a T = 0, CDD pole, the T = 0 scattering length ( a o) = −0.8. the T = 2 scattering length ( a 2) = −0.4. Solution B has a T = 0 and a T = 2. CDD pole, a o ≈ +1 and a 2 ⪅ 0. There is an S-wave resonance in the region 3 m π to 8 m π for T = 0. Solution B is in qualitative agreement with the experimental evidence.
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