A chiral model for bar{q}q and bar{q}bar{q}qq$ mesons

Abstract

We point out that the spectrum of pseudoscalar and scalar mesons exhibits a cuasi-degenerate chiral nonet in the energy region around 1.4 GeV whose scalar component has a slightly inverted spectrum. Based on the empirical linear rising of the mass of a hadron with the number of constituent quarks which yields a mass around $1.4 $GeV for tetraquarks, we conjecture that this cuasi-chiral nonet arises from the mixing of a chiral nonet composed of tetraquarks with conventional bar{q}q states. We explore this possibility in the framework of a chiral model assuming a tetraquark chiral nonet around 1.4 GeV with chiral symmetry realized directly. We stress that U_{A}(1) transformations can distinguish bar{q}q from tetraquark states, although it cannot distinguish specific dynamics in the later case. We find that the measured spectrum is consistent with this picture. In general, pseudoscalar states arise as mainly bar{q}q states but scalar states turn out to be strong admixtures of bar{q}q and tetraquark states. We work out also the model predictions for the most relevant couplings and calculate explicitly the strong decays of the a_{0}(1450) and K_{0}^*(1430) mesons. From the comparison of some of the predicted couplings with the experimental ones we conclude that observable for the isovector and isospinor sectors are consistently described within the model. The proper description of couplings in the isoscalar sectors would require the introduction of glueball fields which is an important missing piece in the present model.