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Combined study of the isospin-violating decay D^*_s→ D_s π⁰ and radiative decay D^*_s→ D_sγ with intermediate meson loops · arXivDesk

2503.13138Mar 17, 202515 pages, 8 figures; Extended version to combine the D_s^* radiative decay; title changed; version accepted by PRD

Combined study of the isospin-violating decay $D^{}_{s}\to D_{s} π^0$ and radiative decay $D^_s\to D_sγ$ with intermediate meson loops

Jun Wang, Qiang Zhao

Phenomenology Experiment

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We carry out a combined study of the isospin-violating decay $D_{s}^{*} \to D_{s} π^{0}$ and radiative decay $D^*_s\to D_sγ$

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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

η-π^{0}

mixing at the tree level the isospin-violating decay

D_{s}^{*} \to D_{s} π^{0}

can be well constrained. In our approach the higher order corrections to the isospin-violating effects can involve the intermediate

D^{(*)}

and

K^{(*)}

scatterings. We find that the contributions from the destructive interference of intermediate meson loops via

D^{(*)0}(c\bar{u}){K}^{(*)+}(u\bar{s})

and

D^{(*)+}(c\bar{d}){K}^{(*)0}(d\bar{s})

rescatterings are significant. Within the commonly accepted ultra-violet (UV) cutoff range we obtain the partial decay width

Γ[D_{s}^{*} \to D_{s} π^{0}] = 9.92^{+0.76}_{-0.66}\,\mathrm{eV}

. This approach allows us to describe the

D_s^*

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}^{*} \to D_{s} π^{0}

D^*_s\to D_sγ

. It then leads to a reliable estimate of the total decay width of

D_s^*

, i.e.

Γ_{\text{total}}(D_s^{*+})=170^{+ 13}_{-12}\,\mathrm{eV}

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