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

TL;DR

This paper proposes that triangle singularity mechanisms can explain the large isospin violations and narrow peaks observed in $ ext{J/}\psi$ decays involving $ ext{eta}(1405/1475)$, shedding light on their nature and related meson mixing.

Contribution

It introduces the triangle singularity mechanism as an explanation for anomalous isospin violations and the long-standing puzzle of $ ext{eta}(1405)$ and $ ext{eta}(1475)$ states.

Findings

Triangle singularity can produce narrow enhancements near $Kar{K}$ thresholds.

Different invariant mass spectra for $ ext{eta}(1405/1475) o a_0(980) ext{pi}$ and $Kar{K}^*+c.c.$ are explained.

The mechanism offers insights into the nature of $ ext{eta}(1405/1475)$ and meson mixing.

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 $K\bar{K}^*+c.c.$, 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 $f_0(980)$.