Radial excitations in the analysis of φ-ω andη−η′mixing

We continue our studies of a unified model of meson structure that makes use 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 mass matrix.) Here we study φ-ω and $\eta -{\eta }^{\prime }$ mixing. The latter study requires that we include the ’t Hooft interaction in our model. We study states of $\overline{q}q$ structure for energies $P^2<~3{\mathrm{GeV}}^2.$ The coupled φ-ω system exhibits ideal mixing, such that the ω and its radially-excited states have no strange quark content, while the φ states are pure $s\overline{s}$ configurations. In the case of $\eta -{\eta }^{\prime }$ mixing, the ’t Hooft interaction gives rise to a $P^2$-dependent mixing angle ${\theta }_P{(P}^2).\mathrm{}$ At the energy of the η(547), ${\theta }_P{(m}_{\eta }^2)=-11.5°,$ while at the energy of the ${\eta }^{\prime }\mathrm{}\left(958\right),$ we have ${\theta }_P{(m}_{{\eta }^{\prime }}^2)=-36.3°,$ if we take singlet-octet mixing into account. We obtain a satisfactory fit to experimental values for energies of the radially-excited states of the φ-ω system, as well as for the decay constants of the ω(782) and the φ(1020). The predictions for the radially-excited $\overline{q}q$ states of the η and ${\eta }^{\prime }$ are not as good, if those states are to be identified as the η(1295) and η(1440). [However, we do find a state at 1370 MeV which is halfway between the η(1295) and η(1440). That suggests the presence of a non-$q\overline{q}$ state that could mix with our state at 1370 MeV to produce the two states at 1295 and 1440 MeV. The state at 1370 MeV is found to have very little $s\overline{s}$ component. Thus one might suggest a correspondence with the ω(1420), which is also a $2S$ state.] Further work is needed to understand the spectrum of the $\eta -{\eta }^{\prime }$ system of states above $P^2=1.0\mathrm{}{\mathrm{GeV}}^2,$ where one may encounter low-energy pseudoscalar 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 spectrum obtained with singlet-octet mixing is largely unchanged upon addition of pseudoscalar-axialvector mixing, if a small value for the strength of the ’t Hooft interaction is used. A small ’t Hooft interaction implies ideal mixing for the $\eta -{\eta }^{\prime }$ pair. It remains to be seen if the wave functions in this case are consistent with experimental...