Isospin violating decay $D^*_s \to D_s π^0$ in chiral perturbation theory

We systematically calculate the isospin violating decay, $D_s^*\to D_sπ^0$, with the heavy meson chiral perturbation theory up to $\mathcal{O}(p^3)$ including the loop diagrams. The $\mathcal{O}(p^3)$ tree level amplitudes contain four undetermined LECs. We use two strategies to estimate them. With the nonanalytic dominance approximation, we get $Γ[D_s^\ast\to D_sπ^0]=(3.38\pm0.12)$ eV. With the naturalness assumption, we give a possible range of the isospin violating decay width, $[1.11-6.88]$ eV. We find that the contribution of the $\mathcal{O}(p^3)$ corrections might be significant.

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