The puzzle of anomalously large isospin violations in $\hat{I}\cdot (1405/1475)\to 3\ddot{I}€$

Abstract

The BES-III Collaboration recently report the observation of anomalously large isospin violations in $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}\cdot (1405/1475)\to {\hat{I}}^3\ddot{I}{€}^0{f}_0(980)\to {\hat{I}}^3+3\ddot{I}€$, where the $f_0(980)$ in the $\ddot{I}€\ddot{I}€$ 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 $\hat{I}\cdot (1405/1475)\to a_0(980)\ddot{I}€$ and $K{\bar{K}}^{\ast }+c.c.$, which can possibly explain the long-standing puzzle about the need for two close states $\hat{I}\cdot (1405)$ and $\hat{I}\cdot (1475)$ in $\hat{I}\cdot \ddot{I}€\ddot{I}€$ and $K\bar{K}\ddot{I}€$, respectively. The TS could be a key to our understanding of the nature of $\hat{I}\cdot (1405/1475)$ and advance our knowledge about the mixing between $a_0(980)$ and $f_0(980)$.

4 pages and 7 eps figures; Journal-matched version