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

Abstract

The BES-III Collaboration recently report the observation of anomalously large isospin violations in $J/ψ\to γη(1405/1475) \to γπ^0 f_0(980)\to γ+3π$, where the $f_0(980)$ in the $ππ$ 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 $η(1405/1475)\to a_0(980)π$ and $K\bar{K}^*+c.c.$, which can possibly explain the long-standing puzzle about the need for two close states $η(1405)$ and $η(1475)$ in $ηππ$ and $K\bar{K}π$, respectively. The TS could be a key to our understanding of the nature of $η(1405/1475)$ and advance our knowledge about the mixing between $a_0(980)$ and $f_0(980)$.