Zweig-superconvergence relations in meson collisions

Abstract

Duality is generally accepted as an important tool in our present understanding of hadron physics. Its origin can be traced back to the successful application of finite energy sum rules (FESR) to the charge exchange pion-nucleon scattering ten years ago ('). Since then the qualitative interconnections among the s-, u-channel resonances and the t-channel Regge poles is firmly established. More quanti tat ive approaches have been subsequently attempted. In particular, ADEMOLLO et al. (2) have shown how precisely the idea of duality works in meson-meson collisions (a). In these cases the resonant part of the amplitude presents no serious ambiguities. On the contrary, the Regge description of the t-channel requires a more or less arbitrary parametrization of the residue functions /~(t), somehow expoiling the striking agreement. In order to avoid this kind of uncertainties the particular type of processes having a vanishing Regge contribution has to be considered. Pioneering work in this direction had already been performed by DE ALFARO et al. (4) in the context of pseudoscalar vector meson scattering. Due to helicity arguments some of the invariant amplitudes have no t-channel exchange and a superconvergent relation (SCR) is obtained among the involved resonances parameters. Since these reactions with several vector particles are complicated by the presence of many independent amplitndcs more attention has been devoted to processes with a different type of exoticism in the t-clmnnel. Thus, many SCR have been constructed exploiting the factorization of reggeon exchanges or, more frequently, making use of arguments based on S U 3 symmetry (5). In this paper we proceed along this direction analysing the s-channel reaction r:K-~ ~K. Its t-channel is exotic since the only allowed Regge trajectory, the p-trajectory, uncouples at the 9~p vertex due to the Zweig rule. This gives rise to a new type