Understanding the property of $\eta (1405/1475)$ in the $J/\psi$ radiative decay

Abstract

In this work we make a systematic analysis of the correlated processes $J/\psi \to \gamma \eta (1440)/f_1(1420)$ with $\eta (1440)/f_1(1420)\to K\bar{K}\pi$, $\eta \pi \pi$ and $3\pi$, 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 $\pi \pi$ invariant mass spectrum of $\eta (1440)\to 3\pi$ with anomalously large isospin violations. Nevertheless, we explicitly demonstrate that the TSM can produce obvious peak position shifts for the same $\eta (1440)$ or $f_1(1420)$ state in different decay channels. This is a strong evidence that the $\eta (1405)$ and $\eta (1475)$ are actually the same state, i.e. $\eta (1440)$. We also make an analysis of the radiative decays of $\eta (1440)\to \gamma V$ ($V=\varphi$, ${\rho }^0$ or $\omega$) 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 $\eta (1405)$ and $\eta (1475)$.

Comments: Revtex, 17 pages and 7 eps figures; revised version to appear in PRD