Relativistic Quark Model Based on the Veneziano Representation. I. Meson Trajectories

Abstract

We base a bootstrap dynamical scheme on the Veneziano model, We assume that the internal trajectories in all channels are similar in their spin and isotopic-spin properties to the external particles, and that vertices are symmetric in their internal and external particles. It turns out that quarks form a very useful entity for expressing the solution, even though the system contains no physical quarks. The spin and multiplicity of the quarks are not determined by the solution, but must be assumed. The spectrum of particles is the same as that predicted by the nonrelativistic quark model, and the particles from multiplets of $\mathrm{SU}\left(6\right)\mathrm{}$. The trajectories of the system, on the other hand, form multiplets of $\mathrm{SU}\left(12\right)\mathrm{}$ or $\mathrm{SU}(6,6)\mathrm{}$, and they are doubled both in their parity and in their Toller $M$ value. Some of the trajectories have residues whose sign corresponds to repulsion rather than attraction, and an interpretation of such trajectories is suggested. If we assume $\rho$ universality in order to fix certain parameters, we can determine all further coupling constants to within a scale factor, and our vertices are those predicted by $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$. In much of the work the detailed form of the Veneziano model is not used, and a comparison is given with certain previous approaches.