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

Abstract

We investigate the dynamical generation of the $D_{s0}^*(2317)$ and $B_{s0}^*$ 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 $D_{s0}^*(2317)$ 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 $D_{s0}^*(2317)$ state emerges from the coupled channels. Our findings reveal that the pole positions of the $D_{s0}^*(2317)$ meson are at $\sqrt{s_R}=(2317.9 - i 0.0593)$ MeV and the $\bar{B}_{s0}^*$ 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 $D_{s0}^*(2317)$ meson as a $DK$ molecular state within the present coupled-channel formalism. In addition, we discuss a possible existence of $\bar{B}_{s0}^{*}$.