(3,3*) direct-sum (3,3*) bilinear symmetry breaking in the linear sigma model

The sigma model with (3,3*) direct-sum (3*,3) bilinear symmetry breaking is studied with a view to find a suitable model smooth in symmetry-breaking parameters. The meson masses and decay constants are treated as functions of xi, the ratio of SU(3) -octet-to-singlet vacuum breaking, which is varied from -2.0 to +2.0. The symmetry-breaking Lagrangian is discussed under various approximations resulting in two-, three-, and four-parameter models. We find that one of the two-parameter models is at least as good as the linear model with a larger region of smoothness. The three- and four-parameter models are smooth in one of the solutions. In most of the three-parameter models with F/sub K//F/sub π/ constrained to be between 1 and 1.3, it is predicted that the Lagrangian and vacuum are approximately SU(2) x SU(2) and SU(3) symmetric, respectively, a much discussed feature of the linear model