U(6,6) Dualized quark model predictions for low energy ππ and πN scattering

Abstract

In the context of a U(6,6) dualized quark model discussed by a number of authors recently, the satisfaction of low energy theorems and the resulting predictions for the ππ and πN s-wave scattering lengths are studied. The model is found to lead to results in agreement with the standard analysis of Weinberg for ππ and Tomozawa-Weinberg for πN scattering when the ambiguities associated with daughter levels are suitably treated. In the ππ case, it is found that the “kineton” terms removing parity doubled states on the leading trajectory are responsible for the satisfaction of the Adler condition, thus confirming earlier work, conditions similar to intercept quantization and KSFR relation are seen to appear rather naturally. For πN, the model predicts satisfactorily the (a ₁−a ₃) combination; concerning the (a ₁+2a ₃) combination, the Adler condition leads to constraints on the exchanged trajectories. A comparison is also made with earlier U(6,6), Lagrangian treatments based on simple pole exchange with “contact” terms.