Covariant confinement model for the calculation of the properties of scalar mesons - art. no. 035201

We continue our studies of a relativistic quark model that features chiral symmetry, covariance, and confinement. In this work we apply our model to t he study of scalar-isoscalar mesons. Several of the parameters of the model have been determined in our earlier work, so that only two new parameters are needed for our analysis. We find a good fit to the spectrum of the f(0) mesons, if we add a glueball with energy of about 1700 MeV. In this model we are rather close to "ideal mixing," with the f(0)(980) having the larges t s (s) over bar mixture of 10%. The f(0)(1370) is the nodeless s (s) over bar state, while the f(0)(1500) is a n (n) over bar=(u (u) over bar+d (d) o ver bar)/root 2 state with a single node. [The presence of that node accoun ts for the small width of the f(0)(1500).] The next state is a n (n) over b ar state with two nodes at 1843 MeV. Thus, we identify the f(0)(1770) as th e state with the largest glueball component. It was found that the vacuum p olarization functions that describe coupling to the two-meson and other con tinuum meson channels play an important role in achieving a good fit to the experimentally determined spectrum. In this work we use a Gaussian regulat or in all our calculations of meson decay amplitudes. In the first part of our study we multiply the Gaussian regulator by a P-2-dependent factor that was chosen so as to modify the threshold behavior of our polarization func tions. With that factor in place, we can study the spectrum of f(0) states without introducing the imaginary parts of the polarization functions that describe decay to the two-meson continuum. When we do introduce the imagina ry parts, we use the vacuum polarization functions with unmodified threshol d behavior. The use of the P-2-dependent factor helps to clarify the nature of the f(0)(400-1200), which is seen, in part, to have its origin as a rat her complex threshold effect associated with the rapid increase of the ampl itudes for decay to the pi pi and K (K) over bar channels. [For a full unde rstanding of the f(0)(400-1200) one needs to also consider the role of t-ch annel rho exchange.] The model used in this work is based upon weak quarkon ium-glueball coupling. However, the four-pion decay of the f(0)(1370) and t he f(0)(1500) suggests that these states may be strongly mixed with the glu eball, which may have a large four-pion decay width. It is also possible th at mixing of these states with the f(0)(980) may be important for understan ding the four-pion decay widths. We provide a short discussion of quarkoniu m-glueball mixing in a schematic model. There is not enough information pre sently available to treat that problem in an unambiguous manner.