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We perform calculations for the $\eta_c \to \eta \pi^+ \pi^-$ decay usingelements of SU(3) symmetry to see the weight of different trios ofpseudoscalars produced in this decay, prior to the final state interaction ofthe mesons. After that, the interaction of pairs of mesons, leading finally to$\eta \pi^+ \pi^-$, is done using the chiral unitary approach. We evaluate the$\pi^+ \pi^-$ and $\pi \eta$ mass distributions and find large and clearsignals for $f_0(500)$, $f_0(980)$ and $a_0(980)$ excitation. The reaction issimilar to the $\chi_{c1} \to \eta \pi^+ \pi^-$, which has been recentlymeasured at BESIII and its implementation and comparison with these predictionswill be very valuable to shed light on the nature of the low mass scalarmesons.

Predictions for $\eta_c \to \eta \pi^+ \pi^-$ producing $f_0(500)$, $f_0(980)$ and $a_0(980)$