Toy model for two chiral nonets

Motivated by the possibility that nonets of scalar mesons might be described as mixtures of "two quark" and "four quark" components, we further study a toy model in which corresponding chiral nonets (containing also the pseudoscalar partners) interact with each other. Although the "two quark" and "four quark" chiral fields transform identically under SU(3)$_L \times$ SU(3)$_R$ transformations they transform differently under the U(1)$_A$ transformation which essentially counts total (quark + antiquark) content of the mesons. To implement this we formulate an effective Lagrangian which mocks up the U(1)$_A$ behavior of the underlying QCD. We derive generating equations which yield Ward identity type relations based only on the assumed symmetry structure. This is applied to the mass spectrum of the low lying pseudoscalars and scalars. as well as their "excitations". Assuming isotopic spin invariance, it is possible to disentangle the amount of"two quark" vs."four quark" content in the pseudoscalar $\pi, K ,\eta$ type states and in the scalar $\kappa$ type states. It is found that a small "four quark" content in the lightest pseudoscalars is consistent with a large "four quark" content in the lightest of the scalar $\kappa$ mesons. The present toy model also allows one to easily estimate the strength of a "four quark" vacuum condensate. There seems to be a rich and interesting structure.Comment: Numerical results updated, typos corrected, references update

Two chiral nonet model with massless quarks

We present a detailed study of a linear sigma model containing one chiral nonet transforming under U(1)$_A$ as a quark-antiquark composite and another chiral nonet transforming as a diquark-anti diquark composite (or, equivalently from a symmetry point of view, as a two meson molecule). The model provides an intuitive explanation of a current puzzle in low energy QCD: Recent work has suggested the existence of a lighter than 1 GeV nonet of scalar mesons which behave like four quark composites. On the other hand, the validity of a spontaneously broken chiral symmetric description would suggest that these states be chiral partners of the light pseudoscalar mesons, which are two quark composites. The model solves the problem by starting with the two chiral nonets mentioned and allowing them to mix with each other. The input of physical masses in the SU(3) invariant limit for two scalar octets and an "excited" pion octet results in a mixing pattern wherein the light scalars have a large four quark content while the light pseudoscalars have a large two quark content. One light isosinglet scalar is exceptionally light. In addition, the pion pion scattering is also studied and the current algebra theorem is verified for massless pions which contain some four quark admixture.Comment: 22 pages, 8 figure

Mass Uncertainties of f0(600) and f0(1370) and their Effects on Determination of the Quark and Glueball Admixtures of the I=0 Scalar Mesons

Within a nonlinear chiral Lagrangian framework the correlations between the quark and glueball admixtures of the isosinglet scalar mesons below 2 GeV and the current large uncertainties on the mass of the f0(600) and the f0(1370) are studied. The framework is formulated in terms of two scalar meson nonets (a two-quark nonet and a four-quark nonet) together with a scalar glueball. It is shown that while some properties of these states are sensitive to the mass of f0(600) and f0(1370), several relatively robust conclusions can be made: The f0(600), the f0(980), and the f0(1370) are admixtures of two and four quark components, with f0(600) being dominantly a non-strange four-quark state, and f0(980) and f0(1370) having a dominant two-quark component. Similarly, the f0(1500) and the f0(1710) have considerable two and four quark admixtures, but in addition have a large glueball component. For each state, a detailed analysis providing the numerical estimates of all components is given. It is also shown that this framework clearly favors the experimental values: m[f0(600)] < 700 MeV and m[f0(1370)] = 1300-1450 MeV. Moreover, an overall fit to the available data shows a reciprocal substructure for the f0(600) and the f0(1370), and a linear correlation between their masses of the form m [f0(1370)] = 0.29 m[f0(600)] + 1.22 GeV. The scalar glueball mass of 1.5-1.7 GeV is found in this analysis.Comment: placement of figures inside text improved. Content unchange

Chiral Nonet Mixing in pi pi Scattering

Pion pion scattering is studied in a generalized linear sigma model which contains two scalar nonets (one of quark-antiquark type and the other of diquark-antidiquark type) and two corresponding pseudoscalar nonets. An interesting feature concerns the mixing of the four isosinglet scalar mesons which yield poles in the scattering amplitude. Some realism is introduced by enforcing exact unitarity via the K-matrix method. It is shown that a reasonable agreement with experimental data is obtained up to about 1 GeV. The poles in the unitarized scattering amplitude are studied in some detail. The lowest pole clearly represents the sigma meson (or f0(600)) with a mass and decay width around 500 MeV. The second pole invites comparison with the f0(980) which has a mass around 1 GeV and decay width around 100 MeV. The third and fourth poles, resemble some of the isosinglet state in the complicated 1-2 GeV region. Some comparison is made to the situation in the usual SU(3) linear sigma model with a single scalar nonet