Continuum bound states K-long, D_{1}(2420), D_{s1}(2536) and their partners K-short, D_{1}(2400), D*_{sJ}(2463)

The very recently observed $D_{sJ}^{\ast }(2463)$ meson is described as a $J^P=1^{+}$ $c\bar{s}$ bound state in a unitarised meson model, owing its existence to the strong OZI-allowed ${}^3{P}_0$ coupling to the nearby $S$-wave $D^{\ast }K$ threshold. By the same non-perturbative mechanism, the narrow axial-vector $D_{s1}(2536)$ resonance shows up as a quasi-bound-state partner embedded in the $D^{\ast }K$ continuum. With the same model and parameters, it is also shown that the preliminary broad $1^{+}$ $D_1(2400)$ resonance and the established narrow $1^{+}$ $D_1(2420)$ may be similar $c\bar{n}$ partners, as a result of the strong OZI-allowed ${}^3{P}_0$ coupling to the nearby $S$-wave $D^{\ast }\pi$ threshold. The continuum bound states $D_1$(2420) and $D_{s1}(2536)$ are found to be mixtures of 33% ${}^3{P}_1$ and 67% ${}^1{P}_1$, whereas their partners $D_1(2400)$ and $D_{sJ}^{\ast }(2463)$ have more or less the opposite ${}^{2S+1}{P}_1$-state content, but additionally with some $D^{\ast }\pi$ or $D^{\ast }K$ admixture, respectively. The employed mechanism also reproduces the ratio of the $K_L$-$K_S$ mass difference and the $K_S$ width, by describing $K_L$ as a bound state embedded in the $\pi \pi$ continuum. The model’s results for $J^P=1^{+}$ states containing one $b$ quark are also discussed.