Abstract
It is shown that, under reasonable assumptions about inelasticity and asymptotic behavior, the usual diffraction picture combined with the N/D approach to π-π scattering leads to a singular integral equation. The authors' formalism is then used to show that, in conformity with the nearby-singularities philosophy, a constant left-hand discontinuity is by itself incapable of producing resonances in the GeV region. Next, a model for the creation of vector resonances, which combines a long-range force (defined by exchange of a cutoff vector meson) plus a short-range force (compatible with diffraction requirements), is introduced. The effect of the short-range force on the self-consistent (bootstrap) solutions is investigated in an approximate scheme. For a self-consistent solution with the correct ρ-meson mass, which is found to exist, inclusion of the short-range force is shown to decrease the self-consistent width by a factor of 2, which is nevertheless still greater than the experimental value.
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