On Compositeness of $D_{s0}^*(2317)$ and its decay to $D_s\pi^0$

Abstract

We demonstrate that the $D_{s0}^{*}(2317)$ can be described as a bound-state pole arising from the coupling between a discrete $c\bar{s}(1^3P_0)$ state and the $DK$ continuum state in the Lee-Friedrichs model. The elementariness and compositeness of the $D_{s0}^{*}(2317)$ are determined to be about $Z:X\approx 51.1 \%:48.9\%$, indicating a nearly equal admixture of compact quark-model state and hadronic molecular components. The decay width of $D_{s0}^{*}(2317)\rightarrow D_s^{+}\pi^0$ is evaluated within the quark rearrangement framework. The transition $c\bar{s}(1^3P_0)\rightarrow D_s\pi^0$ proceeds via the OZI-allowed $c\bar{s}(1^3P_0)-D_s\eta$ coupling followed by $\eta-\pi^0$ mixing, which serves as the primary source of isospin violation in this channel. The coupling between $DK$ and $D_s\pi^0$ is computed in a quark rearrangement model, where the isospin violation effect originates from the mass difference between the $D^0K^+$ and $D^+K^0$ thresholds. The parameters of the scheme shares the same ones with those of the underlying potential model and only the vacuum production strength is adjusted to reproduce the physical $D_{s0}^{*}(2317)$ mass. This calculation may shed more insight to the nature of exotic $D_{s0}^{*}(2317)$ state and its isospin-breaking decay properties.