Abstract
Relaxing the requirements of strict local duality and exact crossing symmetry we examine the predictions of the lowest-moment finite-energy sum rules forππ scattering, taking into account only the leading normal Regge trajectories(ϱ, f 0) and their lower recurrences. Crossed-channel trajectories computed from narrow-resonance saturated sum rules are shown to be linear at large t with a universal slope linked to the choice of Regge-resonance matching energy, and numerical calculations bear this out. It is found that for a range of t the constraints on the ϱ and f 0 Regge poles implied by duality plus the absence of exotic states can be quite well satisfied without introducing towers of daughter resonances. This leads to the suggestion that perhaps duality predictions about lower-lying trajectories should not be taken too seriously.
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