The coupling of π and A 1 trajectories by duality

Abstract

Duality sum rules implied by the absence of resonances in the scattering of pseudoscalar-pseudoscalar, pseudoscalar-vector and vector-vector meson states in channels with exotic quantum numbers are studied. It is shown that the assumption of exact duality and SU(3) symmetry for the vertices leads inevitably to a decoupling of the π and the A 1 Regge trajectories. Next the view is taken that the experimental exchange degeneracy of the π and A 1 trajectories is not accidental and an alternative solution is proposed. It incorporates the normal degeneracy pattern for the leading vector and tensor trajectories but has a coupled triplet of exchange degenerate trajectories ( J PC = 0 ft∓ , 1 ++ and 1 +−) at the secondary level. The implications of this solution for (i) meson spectroscopy, (ii) meson-meson-reggeon coupling and (iii) the breaking of duality are investigated.