On the widths of $η(1295)$ and $η(1405/1475)$

Abstract

Based on the assignment of the first radial excitation states of the isoscalar pseudoscalars for $η(1295)$ and $η(1405/1475)$, we investigate their three-body and four-body decay contributions to the total widths. In agreement with our previous studies we find that the triangle singularity (TS) mechanism arising from the intermediate $K^*\bar{K}$ rescatterings by exchanging a kaon or pion plays a crucial role in both $K\bar{K}π$ and $ηππ$ channels. For the $η_X$ ($η_X$ stands for $η(1295)$ and $η(1405/1475)$) decays into $K\bar{K}π$, we find that although the transition $η_X\to K^*\bar{K}+c.c.\to K\bar{K}π$ is the dominant tree-level process, the productions of the intermediate $K\barκ+c.c.$ and $a_0(980)π$ are strongly enhanced by the TS mechanism. For the $η_X$ decays into $ηππ$, we find that the production of the intermediate $a_0(980)π$ via the triangle transition is the dominant one for $η(1295)$ partly because of the large $η(1295)K^*\bar{K}$ coupling. In contrast, the tree-level and triangle loop contributions are compatible and dominant in the $η(1405/1475)$ decays into $ηππ$. It shows that a combined analysis is useful for disentangling the underlying dynamics for these two states.

17 pages and 7 figures