The $D_{s0}^*(2317)^+$ decay to $D_s^+π^0$ and $D_s^{*+}γ$

TL;DR

This work analyzes the decays of $D_{s0}^*(2317)^+$ to $D_s^+\pi^0$ and $D_s^{*+}\gamma$ within a molecular picture generated by coupled channels $D^0K^+$, $D^+K^0$, $D_s^+\eta$, and $D_s^+\pi^0$ using a local hidden gauge interaction with vector-meson exchange. The strong width is obtained via both a coupled-channel loop and a triangle mechanism, yielding $\Gamma(D_{s0}^*\to D_s^+\pi^0)\approx 70\ \mathrm{keV}$, while the radiative width is computed including charged-current, contact, and anomalous contributions, giving $\Gamma(D_{s0}^*\to D_s^{*+}\gamma)\approx 1.33\ \mathrm{keV}$ with anomalous terms being negligible. The ratio $R = \Gamma_{\gamma}/\Gamma_{\pi^0}$ is $\approx 0.019$, below the Belle-II measurement of $R = (7.14 \pm 0.70 \pm 0.23) \times 10^{-2}$, indicating a tension that calls for precise independent measurements of both decay widths. The results support a molecular interpretation with a substantial $DK$ component but do not resolve the discrepancy with experiment, emphasizing the need for improved data to clarify the $D_{s0}^*(2317)^+$ structure.

Abstract

We study the strong decay of $D_{s0}^*(2317)^+$ to $D_s^+ π^0$ considering the coupled channels of $D^0 K^+, D^+ K^0, D_s^+ η$ and $D_s^+ π^0$ within a picture for the interaction based on the local hidden gauge approach. We also address the problem of the radiative decay to $D_s^{*+} γ$, using the same information obtained from the molecular picture. We obtain a strong width of the $D_{s0}^*(2317)^+$ of about $71 \,\rm keV$ and a radiative decay of $1.3 \,\rm keV$. The anomalous terms for the radiative decay are considered for the first time, but they are found negligible. We make a thorough discussion of this and other results to the light of the recent measurement of Belle for the ratio of these two decay modes, and make a call for the precise measurement of the two decay widths independently to clarify the present situation concerning the nature of of the $D_{s0}^*(2317)^+$ state.

Figures (7)

• Figure 1: Diagrammatic representation of vector exchange as a source of the interaction between two pseudoscalars.
• Figure 2: Diagrams entering the evaluation of the coupling of $D_{s0}(2317)^+$ to $D_s^+ \pi^0$, with the momenta of the particles in parenthesis.
• Figure 3: Diagrams involved in the $D_{s0}^{*}(2317)^+$ decay to $D_s^{*+} \gamma$, involving the charge coupling of the photons to the mesons. In parenthesis the momenta of the particles.
• Figure 4: Diagrams for the charge coupling of a photon to a meson.
• Figure 5: Meson in flight $(a)$ and contact term $(b)$ required by gauge invariance.