5 v 3 1 6 Ju n 20 03 Observed D s ( 2317 ) and tentative D ( 2100 – 2300 ) as the charmed cousins of the light scalar nonet

The very recently observed D∗ sJ (2317) meson is described as a quasi-bound scalar cs̄ state in a unitarized meson model, owing its existence to the strong P0 OZI-allowed coupling to the nearby S-wave DK threshold. By the same mechanism, a scalar D∗ 0(2100– 2300) resonance is predicted above the Dπ threshold. These scalars are the charmed cousins of the light scalar nonet f0(600), f0(980), K ∗ 0 (800), and a0(980), reproduced by the same model. The standard cn̄ and cs̄ charmed scalars D0 and Ds0, cousins of the scalar nonet f0(1370), f0(1500), K ∗ 0 (1430), and a0(1450), are predicted to lie at about 2.64 and 2.79 GeV, respectively, both with a width of some 200 MeV. The D∗ sJ (2317) (or simply Ds(2317)) charmed meson, just discovered [1] by the BABAR collaboration (see also Ref. [2]), is claimed [3] to “send theorists back to their drawing boards,” in view of its low mass. If indeed the tentative J = 0 assignment gets confirmed, there appears to be a discrepancy with typical quark potential models, which predict a mass of 2.48 [4] or 2.49 GeV [5] for this state. The aim of this Letter is to demonstrate that there is no difficulty [6] to obtain a low-mass scalarDs(2317), with a standard cs̄ configuration, provided one takes into account its OZI-allowed 1 coupling to the nearby but closed DK threshold at about 2.36 GeV. The strong P0 coupling to this S-wave threshold will turn out to conjure up a nonperturbative pole, not related to the confinement spectrum, which is forced to settle down on the real energy axis due to the lack of phase space. Conversely, the same threshold pushes the ground-state confinement pole to much higher energies, which may thus have precluded its detection so far. By the same token and as a spin-off, we shall also predict two additional charmed scalar mesons, i.e., with a cn̄ (n = u or d) configuration, still needing experimental confirmation. The mechanism responsible for the low-mass charmed scalar mesons is precisely the same that produces the light scalar-meson nonet, i.e., the f0(600), f0(980), a0(980) [7], and K ∗ 0 (800) [8]. The latter scalar mesons were predicted with great accuracy in Ref. [9], in the framework of a unitarized quark model for all mesons. In more detail, and employing a simpler yet less modeldependent formulation, it has been shown [10, 11, 12] how unitarization leads to structures in the scattering amplitude for S-wave meson-meson scattering which are not and even cannot be anticipated by the naive quark model. Especially, from the behavior of the scattering poles near threshold [13,14], we learn that, in the limit of decoupling from the meson-meson continuum, all members of the light scalar-meson nonet disappear into the background. On the other hand, all other mesons end up as genuine qq̄ states in this limit. Now, it is straightforward to apply the latter, simple model to charmed mesons: one just has to replace one of the model’s effective-quark-mass parameters by the charmed mass. If we then take the other parameters fixed, which e.g. yield an excellent fit to the S-wave Kπ phase shifts up to 1.6 GeV [10], then we obtain the movement of complex-energy poles as depicted in Figs. 1 and 2, corresponding to the cn̄ and cs̄ states, respectively. Next, we interpret with some care each of the two figures, in both of which the relevant parts of the complex E plane are depicted, where E represents the total invariant mass for elastic meson-meson scattering in an S wave. Figure 1 refers to Dπ and Fig. 2 to DK scattering. Each figure displays two trajectories, representing the positions, as a function of the overall coupling parameter λ, of the lowest two of an infinity of singularities in the corresponding scattering amplitudes. The S matrix of our unitarized meson model contains, in principle, all possible two-meson scattering channels. In the model of Refs. [9,10,11,12,13,14], one single set of parameters applies to all channels, from the light flavors to bottom. These parameters are: four constituent quark masses, mu = md, ms, mc, and mb, one confinement parameter, ω, one overall coupling constant, λ, and two shape parameters of the transition potential. When studying Dπ elastic scattering, one could then select this particular channel from a