On compositeness of and its decay to

Abstract

We demonstrate that the

can be described as a bound-state pole arising from the coupling between a discrete

$$c\bar{s}(1^3P_0)$$ c s ¯ ( 1 3 P 0 )

state and the DK continuum state in the Lee–Friedrichs model. The elementariness and compositeness of the

$$D_{s0}^{*}(2317)$$ D s 0 ∗ ( 2317 )

are determined to be about

$$Z:X\approx 51.1 \%:48.9\%$$ Z : X ≈ 51.1 % : 48.9 %

, indicating a nearly equal admixture of compact quark-model state and hadronic molecular components. The decay width of

$$D_{s0}^{*}(2317)\rightarrow D_s^{+}\pi ^0$$ D s 0 ∗ ( 2317 ) → D s + π 0

is evaluated within the quark rearrangement framework. The transition

$$c\bar{s}(1^3P_0)\rightarrow D_s\pi ^0$$ c s ¯ ( 1 3 P 0 ) → D s π 0

proceeds via the OZI-allowed

$$c\bar{s}(1^3P_0)-D_s\eta $$ c s ¯ ( 1 3 P 0 ) - D s η

coupling followed by

$$\eta -\pi ^0$$ η - π 0

mixing, which serves as the primary source of isospin violation in this channel. The coupling between DK and

$$D_s\pi ^0$$ D s π 0

is computed in a quark rearrangement model, where the isospin violation effect originates from the mass difference between the

$$D^0K^+$$ D 0 K +

and

$$D^+K^0$$ 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

$$D_{s0}^{*}(2317)$$ D s 0 ∗ ( 2317 )

mass. We examine the sensitivity of our results to the only free parameter, the pair-creation strength

$$\gamma $$ γ

, and discuss the systematic uncertainties associated with the truncation of coupled channels and the underlying phenomenological potential model. This calculation may shed more insight to the nature of exotic

$$D_{s0}^{*}(2317)$$ D s 0 ∗ ( 2317 )

state and its isospin-breaking decay properties.