Multichannel calculation of the very narrow D s0 * (2317) and the very broad D 0 * (2300–2400)

Abstract

Abstract. The narrow D * s0 (2317) and broad D * 0 (2300-2400) charmed scalar mesons and their radial excitations are described in a coupled-channel quark model that also reproduces the properties of the light scalar nonet. All two-meson channels containing ground-state pseudoscalars and vectors are included. The parameters are chosen fixed at published values, except for the overall coupling constant λ, which is fine-tuned to reproduce the D * s0 (2317) mass, and a damping constant α for subthreshold contributions. Variations of λ and D * 0 (2300-2400) pole postions are studied for different α values. Calculated cross sections for S-wave DK and Dπ scattering, as well as resonance pole positions, are given for the value of α that fits the light scalars. The thus predicted radially excited state D * s0 ′ (2850), with a width of about 50 MeV, seems to have been observed already. The very narrow D * s0 (2317) charm-strange scalar meson first observed [1] three years ago has turned out to be the precursor of a series of new discoveries in hadron spectroscopy that have breathed new life into this field. The surprisingly low mass of the D * s0 (2317) itself has given rise to a flurry of theoretical work and speculations, mostly embracing non-standard quark configurations (see e.g. Ref. PACS[2] for a list of references). Moreover, the very broad charmnonstrange partner meson D * 0 (2300-2400) 1 discovered [4] shortly afterwards further added to the confusion, as its Breit-Wigner mass seems of the same order as the mass of the D * s0 (2317), and perhaps even larger [5]. However, the large width (≃ 260 MeV) of the D * 0 (2300-2400) and the conflicting experimental mass determinations leave enough room for a possible reconciliation with the D * s0 (2317) mass. In Ref.[6], we described the quasi-bound D * s0 (2317) and the D * 0 (2300-2400) resonance as P -wave cs and cn (n = u, d) states, respectively, strongly coupled to the lowest S-wave two-meson channel, i.e., DK resp. Dπ. The framework of our calculation was a simple coupled-channel model previously used to fit the S-wave Kπ phase shifts and predict the K * 0 (800) (alias κ) meson [7]. As a result, both the quasi-bound D * s0 (2317) below the DK threshold and the very broad D * 0 (2300-2400) resonance above the Dπ threshold were roughly reproduced, though with a too low-lying D * 0 (2300-2400) pole. Scaling arguments from flavour invariance later allowed to somewhat improve [2,8,9] our predictions, with no new parameters. In the present study (also see Ref.[10]), we ameliorate our coupled-channel description, by including all pseudoscalarpseudoscalar (PP) and vector-vector (VV) channels, via a generalisation of our model that has recently been applied with success [11] to the whole light scalar nonet. The extension to PP and VV channels should allow us to make reliable predictions at least up to ∼ 3 GeV.Inclusion of all (ground-state) PP and VV channels implies that we couple the scalar cs states to DK, D s η, D s η ′ in S waves, and to D * K * , D * s φ in S as well...