Are three flavors special?

Abstract

It has become clearer recently that the regular pattern of three flavor nonets describing the low spin meson multiplets seems to require some modification for the case of the spin 0 scalar mesons. One picture, which has had some success, treats the scalars in a chiral Lagrangian framework and considers them to populate two nonets. These are, in turn, taken to result from the mixing of two ``bare'' nonets, one of which is of quark-antiquark type and the other of two-quark--two-antiquark type. Here we show that such a mixing is, before chiral symmetry breaking terms are included, only possible for three flavors. In other cases, the two types of structure cannot have the same chiral symmetry transformation property. Specifically, our criterion would lead one to believe that scalar and pseudoscalar states containing charm would not have ``four quark'' admixtures. This work is of potential interest for constructing chiral Lagrangians based on exact chiral symmetry which is then broken by well-known specific terms. It may also be of interest in studying some kinds of technicolor theories.