Continuum bound states $K_{L}$, $D_{1}(2420)$, $D_{s1}(2536)$, and their partners $K_{S}$, $D_{1}(2400)$, $D^{\ast}_{sJ}(2463)$

E. van Beveren; G. Rupp

doi:doi:10.1140/epjc/s2003-01465-0

EPJ

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2021 Impact factor 4.991

Particles and Fields

Eur. Phys. J. C 32, 493-499 (2004)
DOI: 10.1140/epjc/s2003-01465-0

Continuum bound states K_L, D₁(2420), D_s1(2536), and their partners K_S, D₁(2400), $D^{\ast}_{sJ}(2463)$

E. van Beveren¹ and G. Rupp²

¹ Centro de Física Teórica, Departamento de Física, Universidade de Coimbra, 3000 Coimbra, Portugal
² Centro de Física das Interacções Fundamentais, Instituto Superior Técnico, Edifício Ciência, 1049-001 Lisboa Codex, Portugal

eef@teor.fis.uc.pt
george@ajax.ist.utl.pt

(Received: 7 June 2003 / Revised version: 20 October 2003/ / Published online: 18 December 2003)

Abstract
The very recently observed $D^{\ast}_{sJ}(2463)$ 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 $D^{\ast}\!K$ 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⁺ D₁(2400) resonance and the established narrow 1⁺ D₁(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 D₁(2420) and D_s1(2536) are found to be mixtures of 33% $^{3\!}P_{1}$ and 67% $^{1\!}P_{1}$ , whereas their partners D₁(2400) and $D^{\ast}_{sJ}(2463)$ 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. .40.Yx, 14.40.Aq, 14.40.Lb, 13.25.Es, 13.25.Ft, 13.75.Lb