Continuum bound states K L, D 1(2420), D s1(2536), and their partners K S, D 1(2400), D * sJ(2463)

Abstract

The very recently observed D * sJ(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 $D^{*}\!K$ 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 $D^{*}\!K$ 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 $D^{*}\!\pi$ 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(2463) have more or less the opposite $^{2S + 1}\!P_1$-state content, but additionally with some $D^{*}\!\pi$ or $D^{*}\!K$ 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.