convention, choose $\theta = 0$ to be the global minimum. We shall investigate what limits cosmology may place on the existence and depth of the second minimum in the next section; we shall find that the constraint is extremely weak. It is quite surprising to us that [*neither terrestrial experiments nor pure theoretical computations in QCD so far tell us anything about a possible second minimum.*]{}

Our statement certainly goes against the conventional point of view as expounded in ref. [@Pagels], for example, which says that the symmetry breaking potential should be linear in the fields, and for [*three*]{} quark flavors should follow the $(3,3^*)+(3^*,3)$ symmetry breaking scheme of Gell-Mann, Oakes and Renner [@GOM]. The main argument seems to be that this is the simplest description which gives reasonable low energy phenomenology. There was some interest in this issue in the 1970’s in regard to three flavor physics. It was found that the addition of symmetry breaking terms bilinear in the scalar fields resulted in low energy phenomenology as good as, or better than, linear terms alone [@bi]. These bilinear terms could have the structure $(3,3^*)+(3^*,3)$ or they could have components of some other group structure. A more recent study 