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

TL;DR

This paper calculates the isospin violating decay width of $D_s^* o D_s o ext{pion}$ using heavy meson chiral perturbation theory up to third order, highlighting the importance of higher-order corrections.

Contribution

It provides a systematic calculation of the decay width including loop diagrams and estimates the undetermined constants using two different strategies.

Findings

Decay width estimated as 3.38 eV with nonanalytic dominance

Range of decay width estimated as 1.11-6.88 eV under naturalness assumption

Higher-order corrections may significantly affect the decay width

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.