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

In this work we make a systematic analysis of the correlated processes J/psi -> gamma eta(1440)/f(1)(1420) with eta(1440)/f(1)(1420) -> K (K) over bar 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) -> 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) -> gamma V (V = phi, 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). DOI: 10.1103/PhysRevD.87.014023