The $D_s^+ \to a_0(980) e^+ \nu_e$ reaction and the $a_0(980)-f_0(980)$ mixing

TL;DR

This paper investigates the isospin violation mechanisms in the decay of $D_s^+$ to $a_0(980)$ and $f_0(980)$, highlighting the role of kaon loops and meson-meson interactions in revealing the nature of these scalar mesons.

Contribution

It identifies the dominant sources of isospin violation in $D_s^+$ decays and demonstrates the reaction's sensitivity to the internal structure of scalar mesons.

Findings

Kaon loop contributions cause isospin violation due to mass differences.

Main isospin breaking arises from meson-meson transition matrix $T$.

Results align with current experimental bounds, suggesting future measurements can elucidate scalar meson nature.

Abstract

We perform a study of the $D_s^+ \to a_0(980)(f_0(980)) e^+ \nu_e$ reactions investigating the different sources of isospin violation which make the production of the $a_0(980)$ possible. We find that loops involving kaons in the production mechanism provide a source of isospin violation since they do not cancel due to the different mass of charged and neutral kaons, but we also find that the main source comes from the breaking of isospin in the meson-meson transition $T$ matrices, which contain information on the nature of the low lying scalar mesons. The reaction is thus very sensitive to the nature of the $a_0(980)$ and $f_0(980)$ resonances. Our results are consistent with the present upper bound for $a_0(980)$ production and only a factor three smaller, indicating that future runs with more statistics should find actual numbers for this reaction from where we can learn more about the origin of the scalar resonances and their nature.