We perform a study of the $$D_s^+ \rightarrow a_0(980)(f_0(980)) e^+ \nu _e$$ D s + → a 0 ( 980 ) ( f 0 ( 980 ) ) e + ν e reactions investigating the different sources of isospin violation which make the production of the $$a_0(980)$$ 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 $$a_0(980)$$ a 0 ( 980 ) and $$f_0(980)$$ f 0 ( 980 ) resonances. Our results are consistent with the present upper bound for $$a_0(980)$$ 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.

We study the $\bar B_s^0 \to J/\psi f_0(980)$ and $\bar B_s^0 \to J/\psi a_0(980)$ reactions, and pay attention to the different sources of isospin violation and mixing of $f_0(980)$ and $a_0(980)$ resonances where these resonances are dynamically generated from meson-meson interaction. We find that the main reason of isospin violation is the isospin breaking in the meson-meson transition $T$ matrices, and the other source is that the loops involving kaons in the production mechanism provide a source of isospin violation because they do not cancel by the different mass of the charged and neutral kaons. We obtain a branching ratio for $a_0(980)$ production of the order of $5 \times 10^{-6}$. Future experiments can address this problem and the production rate and shape of the $\pi^0 \eta$ mass distribution will definitely help to better understand the nature of scalar resonances. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.