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We briefly discuss how the chiral unitary approach in coupled channels and$SU(3)$ symmetry can be used to describe the production of $f_0(500)$,$f_0(980)$ and $a_0(980)$ in the $\chi_{c1} \to \eta \pi^+ \pi^-$ reaction,recently measured by the BESIII collaboration. In this reaction a very strongpeak for the $a_0(980)$ can be seen in the $\eta\pi$ invariant mass, whileclear signals for the $f_0(500)$ and $f_0(980)$ appear in the one of$\pi^+\pi^-$. Next, we show the predictions made with the same model for theanalogous decay $\eta_c \to \eta \pi^+ \pi^-$, which could also be measuredexperimentally. We discuss the differences of these two reactions which areinteresting to test the picture where these scalar mesons are dynamicallygenerated from the interaction of pairs of pseudoscalars. Furthermore, wecomment on a new recent work where the same model was used to study the$a_0(980) - f_0(980)$ mixing in the $\chi_{c1} \to \pi^0 \pi^0 \eta$ and$\chi_{c1} \to \pi^0 \pi^+ \pi^-$ reactions, showing that quantitativeagreement with the experimental measurement of this mixing, also performed byBESIII, can be obtained, revealing interesting aspects of the dynamics of thisprocess and the importance of coupled channels.

Production and mixing of scalar mesons in $\eta_c$ and $\chi_{c1}$ decays