Dual quark models

Abstract

Our first observation was that our bootstrap condition implied, for the scattering of S U (3) q¯q-compounds, a degeneracy of the exchange degenerate q - f, ω - A₂ trajectories. This conclusion holds for a large variety of dynamical models and remained to hold when S U (3) was broken. We then included a quark-spin and showed that, because of the appearance of degenerate ghost trajectories, a consistent bootstrap scheme could not be formulated. Generalized to linear trajectories, a nice feature of the model was the absense of tachyons.

We then introduced L-excitations of the q¯q-system with different masses; for a linear tower, we recovered the Veneziano formula. However, we considered this to be a special case: any finite or infinite number of L-excitations could be provided for. The derivation of Veneziano zeroes from the factorisation of a finite number of L-excitations was briefly sketched.

Ghost-killing finally lead to a (6,¯6; L) π - ρ spectrum; the price one had to pay was to give up Mandelstam analyticity, Regge-behaviour was still correct.

An extension of this scheme to meson-baryon scattering [16, 18] leads to N- and Δ-trajectories with α_gD = α_N+1; N_α and N _γ trajectories appear to be degenerate, the Δ-trajectory is signature degenerate. These features do not agree with the experimentally found spectrum and further theoretical investigations are necessary.

Lectures given at the HEP Summer School on Strong Interaction Physics, University of Toronto, Department of Physics, 1971.