Pseudoscalar–axial-vector mixing for the kaon and its radial excitations

We use a generalized Nambu–Jona-Lasinio (NJL) model to study pseudoscalar–axial-vector mixing for K mesons. As in a corresponding study of the pion, we find a series doublets in the confining field. When the short-range NJL interaction is included, one member of each doublet moves down in energy to a significant extent and has a small mixing angle. (Those states may be said to be “kaonlike,” while the other states may be called “mixed” states.) We find a mixing angle of -7.04° for the kaon and a kaon-quark coupling constant $g_{\mathrm{Kqq}}=\mathrm{8.09.}\mathrm{}$ With these values we find $f_K=115\mathrm{}\mathrm{MeV},$ which is quite close to the experimental value of $113.0\pm 1.3\mathrm{MeV}.$ (In the absence of pseudoscalar–axial-vector mixing, we have $g_{\mathrm{Kqq}}=5.77\mathrm{}$ and $f_K=85.7\mathrm{}\mathrm{MeV}.)$ The experimentally observed state $K\left(1460\right)\mathrm{}$ is a (nodeless) mixed state in our model and is calculated to be at 1369 MeV. (The value of the mass for this state is given in the data tables as being in the vicinity of 1400 or 1460 MeV, depending upon which of two experimental determinations one consid ers.) We find a total of six states with mass less than 2.0 GeV and provide mixing angles and coupling constants for these states.