In this work we make a systematic analysis of the correlated processes $J/\psi \to \gamma \eta (1440)/f_1(1420)$ with $\eta (1440)/f_1(1420)\to K\overline{K}\pi$, $\eta \pi \pi$ 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 [Wu et al. 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 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 light on the long-standing puzzling question about the nature of $\eta (1405)$ and $\eta (1475)$.

• Received 15 November 2012

DOI:https://doi.org/10.1103/PhysRevD.87.014023