Measurements of the Ratio of Partial Widths: \(\Gamma (D^{*+}_{s} \rightarrow D_{s}^{+}\pi ^{0})/\Gamma (D_{s}^{*+} \rightarrow D_{s}^{+}\gamma )\)

The decay of any higher \(c\bar{s}\) meson to \(D_{s}^{+}\pi ^{0}\) violates isospin conservation, thus small partial width. Some theoretical models suggest \(D_{s}^{*+} \rightarrow D_{s}^{+}\pi ^{0}\) proceed via \(\pi ^{0} - \eta \) mixing to conserve isospin but including such consideration also, the radiative decay \(D_{s}^{*+} \rightarrow D_{s}^{+}\gamma \) is still expected to dominate. The Belle II detector provides an opportunity to improve previous measurements with higher data statistics and improved detector performance. In this presentation, we present the feasibility to study the measurement of the ratio of partial widths \(\Gamma (D_{s}^{*+ } \rightarrow D_{s}^{+}\pi ^{0})/\Gamma (D_{s}^{*+} \rightarrow D_{s}^{+}\gamma )\) .