We propose a systematic procedure to study a generalized linear sigma model which can give a physical picture of possible mixing between $q\overline{q}$ and $qq\overline{q}\overline{q}$ low lying spin zero states. In the limit of zero quark masses, we derive the model independent results for the properties of the Nambu-Goldstone pseudoscalar particles. For getting information on the scalars it is necessary to make a specific choice of terms. We impose two plausible physical criteria—the modeling of the axial anomaly and the suppression of effective vertices representing too many fermion lines—for limiting the large number of terms which are allowed on general grounds. We calculate the tree-level spectrum based on the leading terms in our approach and find that it prominently exhibits a very low mass isosinglet scalar state. Finally we point out that the low energy result for scattering of pions continues to hold in the general version of the model.

• Received 15 December 2006

DOI:https://doi.org/10.1103/PhysRevD.76.014011