$a_0(980)$ and $f_0(980)$ excitation in the $D^+ \to \pi^+ \eta \eta $ decay

Abstract

We have made a thorough study of the $D^+ \to \pi^+ \eta \eta $ reaction, recently measured by the BESIII collaboration, which shows an abnormal strength at high invariant masses in the $\pi\eta$ mass distribution. We studied in detail the triangle mechanism and the $f_0(1370)$ excitation modes that have been suggested to explain this abnormal feature, and concluded that they are too small to have any important role in the solution to that problem. We have also studied other possible solutions evaluating the contribution of excitations of other $f_0$, $a_0$ and $f_2$ resonances and reached the same conclusion. Unexpectedly, the solution to the problem is found considering the $f_0(980)$ excitation, with the $f_0(980)$ decaying to two $\eta$, which is tied to the $a_0(980)$ production, and well under control. At the same time, the consideration of the $f_0(980)$ excitation solves another non reported problem, which is the $\eta \eta$ mass distribution that comes when only the $a_0(980)$ resonance is allowed to be excited, which produces a large deficiency at low invariant masses compared with experiment.