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

TL;DR

This study investigates the decay mechanisms of $ ext{eta}(1295)$ and $ ext{eta}(1405/1475)$, emphasizing the role of triangle singularity mechanisms in their three- and four-body decay widths, providing insights into their underlying dynamics.

Contribution

It introduces a detailed analysis of decay contributions, highlighting the significance of triangle singularity mechanisms in the decay processes of these eta states, which was not fully understood before.

Findings

Triangle singularity significantly affects decay widths.

Intermediate $K^*ar{K}$ rescattering enhances certain decay channels.

Different decay mechanisms dominate for $ ext{eta}(1295)$ and $ ext{eta}(1405/1475)$.

Abstract

Based on the assignment of the first radial excitation states of the isoscalar pseudoscalars for $\eta(1295)$ and $\eta(1405/1475)$, 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 $K\bar{K}\pi$ and $\eta\pi\pi$ channels. For the $\eta_X$ ($\eta_X$ stands for $\eta(1295)$ and $\eta(1405/1475)$) decays into $K\bar{K}\pi$, we find that although the transition $\eta_X\to K^*\bar{K}+c.c.\to K\bar{K}\pi$ is the dominant tree-level process, the productions of the intermediate $K\bar{\kappa}+c.c.$ and $a_0(980)\pi$ are strongly enhanced by the TS mechanism. For the $\eta_X$ decays into $\eta\pi\pi$, we find that the production of the intermediate $a_0(980)\pi$ via the triangle transition is the dominant one for $\eta(1295)$ partly because of the large $\eta(1295)K^*\bar{K}$ coupling. In contrast, the tree-level and triangle loop contributions are compatible and dominant in the $\eta(1405/1475)$ decays into $\eta\pi\pi$. It shows that a combined analysis is useful for disentangling the underlying dynamics for these two states.