Three-Body Unitary Coupled-Channel Analysis on $\eta (1405/1475)$

Abstract

The recent BESIII data on $J/\psi \to \gamma (K_S{K}_S{\pi }^0)$, which is significantly more precise than earlier $\eta (1405/1475)$-related data, enables quantitative discussions on $\eta (1405/1475)$ at the previously unreachable level. We conduct a three-body unitary coupled-channel analysis of experimental Monte-Carlo outputs for radiative $J/\psi$ decays via $\eta (1405/1475)$: $K_S{K}_S{\pi }^0$ Dalitz plot distributions from the BESIII, and branching ratios of $\gamma (\eta {\pi }^{+}{\pi }^{-})$ and $\gamma (\gamma {\pi }^{+}{\pi }^{-})$ final states relative to that of $\gamma (K\bar{K}\pi )$. Our model systematically considers (multi-)loop diagrams and an associated triangle singularity, which is critical in making excellent predictions on $\eta (1405/1475)\to \pi \pi \pi$ lineshapes and branching ratios. The $\eta (1405/1475)$ pole locations are revealed for the first time. Two poles for $\eta (1405)$ are found on different Riemann sheets of the $K^{\ast }\bar{K}$ channel, while one pole for $\eta (1475)$. The $\eta (1405/1475)$ states are described with two bare states dressed by continuum states. The lower bare state would be an excited ${\eta }^{\prime }$, while the higher one could be an excited ${\eta }^{(\prime )}$, hybrid, glueball, or their mixture. This work presents the first-ever pole determination based on a manifestly three-body unitary coupled-channel framework applied to experimental three-body final state distributions (Dalitz plots).

Comments: 7 pages, 6 figures; (v2) published version; statistical errors for eta(1405/1475) pole positions are added