Combined study of the isospin-violating decay $D_s^{\ast }\to D_s{\pi }^0$ and radiative decay $D_s^{\ast }\to D_s\gamma$ with intermediate meson loops

Abstract

We carry out a combined study of the isospin-violating decay $D_s^{\ast }\to D_s{\pi }^0$ and radiative decay $D_s^{\ast }\to D_s\gamma$ in an effective Lagrangian approach by taking into account the corrections from the one-loop transitions. By distinguishing the transition mechanisms of the long-distance interactions through the intermediate meson loops from the short-distance interactions through the $\eta -{\pi }^0$ mixing at the tree level the isospin-violating decay $D_s^{\ast }\to D_s{\pi }^0$ can be well constrained. In our approach the higher order corrections to the isospin-violating effects can involve the intermediate $D^{(\ast )}$ and $K^{(\ast )}$ scatterings. We find that the contributions from the destructive interference of intermediate meson loops via $D^{(\ast )0}(c\bar{u})K^{(\ast )+}(u\bar{s})$ and $D^{(\ast )+}(c\bar{d})K^{(\ast )0}(d\bar{s})$ rescatterings are significant. Within the commonly accepted ultra-violet (UV) cutoff range we obtain the partial decay width $\Gamma [D_s^{\ast }\to D_s{\pi }^0]=9.92_{-0.66}^{+0.76}\mathrm{eV}$. This approach allows us to describe the $D_s^{\ast }$ radiative decay in the same framework via the vector meson dominance (VMD) model. We demonstrate that both the tree-level and one-loop transitions can be self-consistently determined if we adopt the experimental data for the branching ratio fraction of $D_s^{\ast }\to D_s{\pi }^0$ to $D_s^{\ast }\to D_s\gamma$. It then leads to a reliable estimate of the total decay width of $D_s^{\ast }$, i.e. ${\Gamma }_{\text{total}}(D_s^{\ast +})=170_{-12}^{+13}\mathrm{eV}$.

arXiv comment15 pages, 8 figures; Extended version to combine the D_s^* radiative decay; title changed; version accepted by PRD

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