Covariant confinement model for the study of the properties of light mesons

We continue our studies of a relativistic quark model that includes a covariant model of confinement. [In the absence of the confinement model, our model reduces to the SU(3)-flavor version of the Nambu–Jona-Lasinio (NJL) model.] In previous works we have studied the radial excitations of the pion, $\eta -{\eta }^{\prime }$ mixing, and ω-φ mixing. Here we extend our work to study the K mesons of the pseudoscalar, vector, and scalar nonets. In addition, we provide some preliminary analysis of the ${}^3{P}_1$ and ${}^1{P}_1$ axial-vector nonets and develop a formalism that enables us to consider ${}^3{P}_1{-}^1{P}_1$ mixing of the strange axial-vector mesons. That is accomplished by adding interactions to the NJL Lagrangian that contain gradients of the quark field. Once the parameters of the model are fixed by fitting the energies of the ω(782), ω(1420), $K\left(495\right),$ and φ(1020), we find the model has significant predictive power. For example, the masses of the $K^{*}\mathrm{}\left(892\right),$ $K_0^{*}\mathrm{}\left(1430\right),$ and $a_1\mathrm{}\left(1260\right)\mathrm{}$ are predicted correctly. For the pseudoscalar nonet we find nineteen states below 2 GeV and for the vector nonet we have eleven states with mass less than 2 GeV. On the whole, the pattern of radial excitations of the various mesons is reproduced in our model.