The $D_{s0}^*(2317)^+$ decay to $D_s^+\pi^0$ and $D_s^{*+}\gamma$

We study the strong decay of $D_{s0}^*(2317)^+$ to $D_s^+ \pi^0$ considering the coupled channels of $D^0 K^+, D^+ K^0, D_s^+ \eta$ and $D_s^+ \pi^0$ within a picture for the interaction based on the local hidden gauge approach. We also address the problem of the radiative decay to $D_s^{*+} \gamma$, using the same information obtained from the molecular picture. We obtain a strong width of the $D_{s0}^*(2317)^+$ of about $77 \,\rm keV$ from coupled channels interaction and a radiative decay of about $1.7 \,\rm keV$. We also show that the extra consideration of $\pi^0-\eta$ mixing can double the strong decay width to values around $140 \,\rm keV$. 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 the $D_{s0}^*(2317)^+$ state.