The puzzle of anomalously large isospin violations in $\eta (1405/1475)\to 3\pi$

Abstract

The BES-III Collaboration recently report 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 MeV) than the peak width ($\sim$50 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 $K\bar{K}$ 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 $K{\bar{K}}^{\ast }+c.c.$, 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 $K\bar{K}\pi$, 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 $f_0(980)$.

Comments: 4 pages and 7 eps figures; Journal-matched version