Abstract
We systematically calculate the isospin violating decay, $D_s^*\to D_s\pi^0$, 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 $\Gamma[D_s^\ast\to D_s\pi^0]=(3.38\pm0.12)$ 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.
Highlights
The DðsÞ mesons are composed of one charm quark and one light antiquark
We obtain the range of the isospin violating decay width as [5.2, 11.7] eV
The dynamics of DðsÞ mesons is constrained by both the chiral symmetry in the light quark sector and the heavy quark symmetry in the heavy sector
Summary
The DðsÞ mesons are composed of one charm quark and one light antiquark. The dynamics of DðsÞ mesons is constrained by both the chiral symmetry in the light quark sector and the heavy quark symmetry in the heavy sector. Decay behaviors of DðsÞ mesons will provide us with very important information about the heavy quark symmetry and the light quark dynamics. Chiral perturbation theory and heavy quark effective theory are used in Refs. Note that DÃs → Dsπ0 is the strong decay process which violates the isospin symmetry. For the DðsÞ mesons, the charm quark mass mc is much larger than the light quark mass mqðq 1⁄4 u; d; sÞ; mc can be integrated out at the low energy scale. [7,8,9,43,44,45,46], the chiral effective theory incorporating heavy quark symmetry was constructed. The chiral Lagrangian describes the low energy strong interactions between the heavy hadrons and light Goldstone bosons.
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