Low Energy π-π Final State Interaction in the Veneziano Model

Abstract

Low energy n-n interaction is studied in the Veneziano model. It is shown that the pure Veneziano model with p trajectory dominance can describe the 1=0, J=O low energy behavior of the n-n system qualitatively. It predicts the existence of e resonance which is considerably broader than the p resonance. The final state interaction effect characterized by two pion intermediate state is considered. It is concluded that the correction is small but in the correct direction for the energy region below e mass. In the e region it has the effect to produce a long shoulder which is favoured by the present experimental data. §I. IntroductionThe Veneziano model has the nice properties that it has correct asymptotic behavior and correct positions of resonances. 1 ) Therefore it usually predicts the correct angular distributions in the high energy limit and at the same time can fit the mass distributions qualitatively in the resonance energy region. However, a Veneziano model that takes care of the physical threshold branch points and satisfies the unitarity condition in a general sense is still lacking. There are some phenomenological models that remedy this defect partially. 2 ) Some of the calculations indicate that the experimental data are compatible with such models. 3 ) However, we may raise an interesting question that .how much has been improved by unitarizing the Veneziano model in some aspects. In the absence of a model that takes care of unitarity in a general sense the answer to the former question depends on the phenomenological model we are working with. In a previous communication we presented a final state interaction model that adds the twoparticle intermediate state contributions to the original Veneziano amplitude. 4 ) It was shown that the resultant amplitude maintains crossing symmetry, the correct high energy behavior and satisfies elastic unitarity condition approximately in the low energy region. The purpose of this work is to apply such a model to the rc-rc system to see how much effect will be produced. In § 2 we shall give a specific description of our model that applies to the rc-rc system. In § 3 we shall present our results of calculation.