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 $K^*\bar{K}^*,\rho\rho,\omega\omega,\phi\phi, \omega\phi,\pi\pi,K\bar{K},\eta\eta$. We show that the pole assigned to $f_0(1710)$ does not change much. Then we calculate the partial decay widths of $f_0(1710) \to K^*\bar{K}^* \to \pi\pi,K\bar{K},\eta\eta$ as the coupled channel dynamically generated state as well as assuming it to be pure $K^*\bar{K}^*$ molecule. In both cases the ratios of partial decay widths agree fairly with that in PDG.
Highlights
More and more hadron resonances have been proposed to be hadron molecules [1] with much more predicted ones to be searched for [2]
We extend the study of f0ð1710Þ by including its coupling to channels of pseudoscalar mesons within the coupled-channel approach
Some recent works [13,14] studied the interaction of the nonet of vector mesons themselves and found a pole with the quantum number JPC 1⁄4 0þþ mainly coupling to the K ÃKÃ channel, possibly corresponding to f0ð1710Þ
Summary
More and more hadron resonances have been proposed to be hadron molecules [1] with much more predicted ones to be searched for [2]. A well-known example is the Λð1405Þ [11], which can be dynamically generated in the vicinity of the πΣ and K−p thresholds. The another example is f0ð980Þ [8,12], which is considered to arise due to ππ and KKcoupled channel interactions. Some recent works [13,14] studied the interaction of the nonet of vector mesons themselves and found a pole with the quantum number JPC 1⁄4 0þþ mainly coupling to the K ÃKÃ channel, possibly corresponding to f0ð1710Þ. The interaction Lagrangian among vector mesons and pseudoscalar mesons is given by [16,17].
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