Abstract

We consider a simple $\ensuremath{\pi}\ensuremath{\pi}$ model in which we first dynamically generate a low- and intermediate-energy absorptive part $A$ and then calculate effective Regge residues in terms of $A$ via finite-energy sum rules (FESR). In an earlier paper, $A$ was calculated by unitarizing the Lovelace-Veneziano model. In the present paper we follow a somewhat less model-dependent procedure. In states and energy regions where no important narrow resonances are present, we evaluate the (background) $A$ by using approximate unitarity and the duality assumption that amplitudes are well approximated on the average by Regge exchange. Elsewhere the resonances ($\ensuremath{\rho}$ and ${f}^{0}$) are put in by hand. Pomeranchuk ($P$) parameters are taken from experiment or calculated from simple models. Exchange degeneracy and two-component duality are not assumed a priori, although we find that exchange degeneracy is approximately satisfied by our output Regge residues at $t=0$. For $t\ensuremath{\ne}0$, on the other hand, we find that it is broken. Specifically, $\ensuremath{\rho}$ exchange is peripheral, as required by the dual absorptive model, whereas $f$ exchange is not; a similar conclusion was reached on purely phenomenological grounds by Barger, Geer, and Halzen for other reactions.

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