Approximate dynamical symmetry in lattice quantum chromodynamics

Abstract

We discuss the phenomenological implications of an approximate SU(6)×SU(6)×U(1) symmetry of hadron physics which remains after dynamical symmetry breaking in the strong-coupling lattice gauge theory. This symmetry is similar to but differs in an essential fashion from previous versions of SU(6) × SU(6) × or $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$. The difference resolves some of the problems of the older schemes—for example, although we obtain the "good" result $\frac{{\mu }_p}{{\mu }_n}=-\frac{3}{2}$, we avoid the "bad" result $\frac{g_A}{g_V}=-\frac{5}{3}$. We find that mesons are better approximated as irreducible representations of an $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$ than static SU(6). Vector mesons are pseudo-Goldstone bosons in our scheme, which explains why the sum rules for their masses should be written in terms of mass squared, like those of the pseudoscalars.