A Resonance Model of Bosons Based on Duality and the Quark Model

Abstract

An s-channel resonance model of bosons for meson-meson scattering in the nonet scheme is proposed on the basis of the quark model and duality in the sense of finite-energy sum rules. Elastic widths of boson resonances in 1rn:, Krr and KK scattering are predicted. Recently it has been shown1> that rm sca:ttering amplitudes deduced from the recent CERN-Munich data2> give strong supports to predictions of the. bootstrap scheme of duality3> that the Regge trajectorie,s spaced by two units of angular­ momenta bootstrap among themselves. The above bootstrap scheme of duality is in accord with th~ L-excitation quark model with weak L · S couplings.'> This quark model description also 'continues to provide us with a most economical framework to explain the observed regularities of rich boson sp.ectrum. Therefore, it is worth while to construct a resonance model of bosons based on duality*> and the boson spectrum of the quark model. The purpose of this paper is to present a phenomenological model of bosons for meson-meson (rm, Kn:, KK) scattering based on duality*> and the quark model from die s-channel point of view in the narrow-width approximation, and to predict elastic widths of these bosons in the framework of the nonet scheme of ideal mixing.5> From the t-channel point of view, however, the imaginary part of our amplitude is not dominated by a simple t-channel Regge pole, but is dominated by some effective t-channel pole presumably due to .poles .and' cuts. 6>