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 masses of f0(600) and 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 masses of f0(600) and f0(1370), several relatively robust conclusions can be made: f0(600), f0(980), and f0(1370) are admixtures of two- and four-quark components, with f0(600) being dominantly a nonstrange four-quark state, and f0(980) and f0(1370) having a dominant two-quark component. Similarly, f0(1500) and f0(1710) have considerable two- and four-quark admixtures, but in addition they 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: mexpt[f0(600)]<700 MeV and mexpt[f0(1370)]=1300-1450 MeV. Moreover, an overall fit to the available data shows a reciprocal substructure for f0(600) and f0(1370), and a linear correlation between their masses of the form m[f0(1370)]=0.29m[f0(600)]+1.22 GeV. The scalar glueball mass of 1.5-1.7 GeV is found in this analysis