Multichannel calculation of the very narrow $D_{s0}^*(2317)$ and the very broad $D_0^*(2300-2400)$

Abstract

The narrow $D_{s0}^{\ast}$(2317) and broad $D_0^{\ast}$(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 $\lambda$, which is fine-tuned to reproduce the $D_{s0}^{\ast}$(2317) mass, and a damping constant $\alpha$ for subthreshold contributions. Variations of $\lambda$ and $D_0^{\ast}$(2300-2400) pole postions are studied for different $\alpha$ values. Calculated cross sections for $S$-wave $DK$ and $D\pi$ scattering, as well as resonance pole positions, are given for the value of $\alpha$ 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.