Two dynamical generated $a_0$ resonances by interactions between vector mesons

TL;DR

This paper investigates the dynamical generation of two $a_0$ resonances through vector meson interactions, revealing their dependence on coupled channels and proposing new states near specific thresholds.

Contribution

It introduces a coupled-channel approach to dynamically generate $a_0$ resonances, including a novel $a_0(1710)$ state and insights into their decay channels.

Findings

The $a_0(1710)$ is generated near the $K^*ar{K}^*$ threshold.

The $a_0(1450)$ may be dynamically generated by $ ho ext{-} ext{omega}$ interactions.

The existence of the $a_0(1710)$ depends on coupled channel effects.

Abstract

We study dynamically generated $a_0$ resonances by interactions between vector mesons including their coupling to channels of pseudoscalar mesons within coupled-channel approach. Both vector and pseudoscalar mesons are considered as $t$-channel exchanged mesons for calculating interactions between vector mesons. Analogous to $a_0(980)$ as a $K\bar K-\pi\eta$ dynamically generated state, there is an $a_0(1710)$ as a coupled channel dynamically generated state near $K^*\bar{K}^*$ threshold. The channels involved are $\rho\phi,K^*\bar{K}^*,\rho\omega, K\bar{K},\pi\eta$. This $a_0$ mainly decays to $\rho\omega$, $\pi\eta$ and $K\bar{K}$. This pole is much tied to the coupled channel effect. If we turn off either $\rho\phi$ or $K^*\bar{K}^*$, the pole disappears. In addition, it is found that $a_0(1450)$ may also be dynamically generated by $\rho\omega$ interactions due to $\pi$ and $\eta$ exchange.