Further study of $f_0(1710)$ with coupled-channel approach and hadron molecular picture

Abstract

The $f_0(1710)$ was previously proposed to be dynamically generated state by interactions between vector mesons. We extend the study of $f_0(1710)$ by including its coupling to channels of pseudoscalar mesons within coupled-channel approach. The channels involved are $K^{\ast }{\bar{K}}^{\ast },\rho \rho ,\omega \omega ,\varphi \varphi ,\omega \varphi ,\pi \pi ,K\bar{K},\eta \eta$. We show that the pole assigned to $f_0(1710)$ does not change much. Then we calculate the partial decay widths of $f_0(1710)\to K^{\ast }{\bar{K}}^{\ast }\to \pi \pi ,K\bar{K},\eta \eta$ as the coupled channel dynamically generated state as well as assuming it to be pure $K^{\ast }{\bar{K}}^{\ast }$ molecule. In both cases the ratios of partial decay widths agree fairly with that in PDG.