The BES-III Collaboration recently reported the observation of anomalously large isospin violations in $J/\psi \to \gamma \eta (1405/1475)\to \gamma {\pi }^0{f}_0(980)\to \gamma +3\pi$, where the $f_0(980)$ in the $\pi \pi$ invariant mass spectrum appears to be much narrower ($\sim 10\mathrm{MeV}$) than the peak width ($\sim 50\mathrm{MeV}$) measured in other processes. We show that a mechanism, named as triangle singularity (TS), can produce a narrow enhancement between the charged and neutral $K\overline{K}$ thresholds, i.e., $2m_{K^{\pm }}\sim 2m_{K^0}$. It can also lead to different invariant mass spectra for $\eta (1405/1475)\to a_0(980)\pi$ and $K{\overline{K}}^{*}+\mathrm{c}.\mathrm{c}.$, which can possibly explain the long-standing puzzle about the need for two close states $\eta (1405)$ and $\eta (1475)$ in $\eta \pi \pi$ and $K\overline{K}\pi$, respectively. The TS could be a key to our understanding of the nature of $\eta (1405/1475)$ and advance our knowledge about the mixing between $a_0(980)$ and $f_0(980)$.

• Received 18 August 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.081803