Covariant calculation of the properties off2mesons in a generalized Nambu–Jona-Lasinio model

We use our covariant model of light-meson structure to study the $f_2$ tensor mesons. Our model is a generalized Nambu–Jona-Lasinio (NJL) model that includes a relativistic model of confinement. For the study of tensor mesons, we extend the NJL model to include interactions that contain gradients of the quark fields. There are two such terms requiring the introduction of two additional coupling constants for the model. We find a good fit to the experimentally determined states. We obtain ten states below 2 GeV, while there are eight states in the data tables with energies less than 2 GeV, if we include the recently found $f_J\mathrm{}\left(1750\right)\mathrm{}$ in our list of $f_2$ mesons. We find $f_2^{\prime }$ states of $s\overline{s}$ structure at 1551, 1745, and 1767 MeV. The first two of these states have nodeless wave functions and may be identified with the $f_2^{\prime }\mathrm{}\left(1525\right)\mathrm{}$ and the $f_J\mathrm{}\left(1750\right),$ if $J=2\mathrm{}$ for the new state. (The state at 1767 MeV is a $2S\hspace{0.5em}s\overline{s}$ state, which may mix with the 1745 MeV state to some degree.) Our analysis suggests a new classification for nonets of radially excited states that is based upon our relativistic model of light-meson structure.