Ambiguity of the Meson-Baryon Couplings in a Bootstrap Static Model ofSU(6)Symmetry

Abstract

In the present discussion we seek to clarify certain aspects of $\mathrm{SU}\left(6\right)\mathrm{}$ theory which have an important bearing on the problem of formulating a bootstrap dynamical description of symmetry breaking. We discuss here, in particular, a certain ambiguity of the meson-baryon coupling which exists even in the limit of exact $\mathrm{SU}\left(6\right)\mathrm{}$ symmetry, and which we call assignment mixing. It is possible to recover certain special theories, such as the so-called $W$-spin theory, by a particular choice of the assignment mixing angles. Bootstrap equations in the exact $\mathrm{SU}\left(6\right)\mathrm{}$ limit do not fix the angles, unless one also considers mesonic bootstrap equations corresponding to Fermi-Yang-type theories. It is also shown that in the exact $\mathrm{SU}\left(6\right)\mathrm{}$ limit, the normalization and vertex equations of the Cutkosky-Leon bootstrap method both yield the same equation, which relates the coupling constant $f$ to the ratio of the meson mass $m$ to the cutoff parameter $k_{\Lambda }$. Approximate solutions of the Bethe-Salpeter equation are obtained.