$D_{s0}^{\ast }(2317)$ and $B_{s0}^{\ast }$ as molecular states

Abstract

We investigate the dynamical generation of the $D_{s0}^{\ast }(2317)$ and $B_{s0}^{\ast }$ mesons using a meson-exchange model with a coupled-channelformalism. Our primary focus is on the $D_s^{+}{\pi }^0$ channel below the $DK$ threshold. First, we construct the invariant kernel amplitudes, incorporating effective Lagrangians based on heavy-quark symmetry, flavor SU(3) symmetry, and hidden local symmetry. Since the $D_{s0}^{\ast }(2317)$ state implies isospin symmetry breaking, we introduce ${\pi }^0-\eta$ isospin mixing. We subsequently solve the coupled-channel integral equations, which include four different channels, i.e., $D_s^{+}{\pi }^0$, $D^0{K}^{+}$, $D^{+}{K}^0$, and $D_s^{+}\eta$. We carefully analyze how the pole corresponding to the $D_{s0}^{\ast }(2317)$ state emerges from the coupled channels. Our findings reveal that the pole positions of the $D_{s0}^{\ast }(2317)$ meson are at $\sqrt{s_R}=(2317.9-i0.0593)$ MeV and the ${\bar{B}}_{s0}^{\ast }$ meson at $(5756.43-i0.0215)$ MeV, respectively. We also discuss their decay widths and destructive interference of the two sources. In conclusion, our current results provide a clear indication supporting the interpretation of the $D_{s0}^{\ast }(2317)$ meson as a $DK$ molecular state within the present coupled-channel formalism. In addition, we discuss a possible existence of ${\bar{B}}_{s0}^{\ast }$.

Comments: 15 pages, 8 figures. Final version for publication in PTEP