Understanding the property of $η(1405/1475)$ in the $J/ψ$ radiative decay

Abstract

In this work we make a systematic analysis of the correlated processes $J/ψ\to γη(1440)/f_1(1420)$ with $η(1440)/f_1(1420)\to K\bar{K}π$, $ηππ$ and $3π$, where the role played by the so-called "triangle singularity mechanism" (TSM) is clarified. Our results agree well with the experimental data and suggest a small fraction of $f_1(1420)$ contributions in these processes. This study confirms our conclusion in [Phys. Rev. Lett. 108, 081803 (2012)] that the dynamic feature of the TSM can be recognized by the strong narrow peak observed in the $ππ$ invariant mass spectrum of $η(1440)\to 3π$ with anomalously large isospin violations. Nevertheless, we explicitly demonstrate that the TSM can produce obvious peak position shifts for the same $η(1440)$ or $f_1(1420)$ state in different decay channels. This is a strong evidence that the $η(1405)$ and $η(1475)$ are actually the same state, i.e. $η(1440)$. We also make an analysis of the radiative decays of $η(1440)\to γV$ ($V=ϕ$, $ρ^0$ or $ω$) which shows that such a one-state prescription seems not to have a conflict with the so-far existing experimental data. Our analysis may shed a light on the long-standing puzzling question on the nature of $η(1405)$ and $η(1475)$.