Radial excitations in the analysis of phi-omega and eta-eta ' mixing

We continue our studies of a unified model of meson structure that makes us e of a Nambu-Jona-Lasinio (NJL) model that has been generalized to include a relativistic model of confinement. (We use Lorentz-vector confinement, so that the Lagrangian exhibits chiral symmetry in the absence of a quark mas s matrix.) Here we study phi-omega and eta-eta' mixing. The latter study re quires that we include the 't Hooft interaction in our model. We study stat es of <(q)over bar q> structure for energies P-2 less than or equal to 3 Ge V2. The coupled phi-omega system exhibits ideal mixing, such that the omega and its radially-excited states have no strange quark content, while the p hi states are pure <s(s)over bar> configurations. In the case of eta-eta' m ixing, the 't Wooft interaction gives rise to a P-2-dependent mixing angle theta(P)(P-2). At the energy of the eta(547), theta(P)(m(eta)(2)) = -11.5 d egrees, while at the energy of the eta'(958), we have theta(P)(m(eta')(2)) = -36.3 degrees, if we take singlet-octet mixing into account. We obtain a satisfactory fit to experimental values for energies of the radially-excite d states of the phi-omega system, as well as for the decay constants of the omega(782) and the phi(1020). The predictions for the radially-excited <(q )over bar q> states of the eta and eta' are not as good, if those states ar e to be identified as the eta(1295) and eta(1440). [However, we do find a s tate at 1370 MeV which is halfway between the eta(1295) and eta(1440). That suggests the presence of a non-<q(q)over bar> state that could mix with ou r state at 1370 MeV to produce the two states at 1295 and 1440 MeV. The sta te at 1370 MeV is found to have very little <s(s)over bar> component. Thus one might suggest a correspondence with the omega(1420), which is also a 2S state.] Further work is needed to understand the spectrum of the eta-eta' system of states above P-2 = 1.0 GeV2, where one may encounter low-energy p seudoscalar glueball states. We extend our work on singlet-octet mixing to include pseudoscalar-axialvector mixing. In that case there are two mixing angles and two coupling constants to be calculated. It is found that the sp ectrum obtained with singlet-octet mixing is largely unchanged upon additio n of pseudoscalar-axialvector mixing, if a small value for the strength of the 't Hooft interaction is used. A small 't Hooft interaction implies idea l mixing for the eta - eta' pair. It remains to be seen if the wave functio ns in this case are consistent with experimental decay rates. [S0556-2813(9 8)04412-4].