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Description of $ρ(1700)$ as a $ρK \bar{K}$ system with the fixed center approximation

We study the $ρK\bar{K}$ system with an aim to describe the $ρ(1700)$ resonance. The chiral unitary approach has achieved success in a description of systems of the light hadron sector. With this method, the $K \bar{K}$ system in the isospin sector $I=0$, is found to be a dominant component of the $f_0 (980)$ resonance. Therefore, by regarding the $K\bar{K}$ system as a cluster, the $f_0 (980)$ resonance, we evaluate the $ρK\bar{K}$ system applying the fixed center approximation to the Faddeev equations. We construct the $ρK$ unitarized amplitude using the chiral unitary approach. As a result, we find a peak in the three-body amplitude around 1739 MeV and a width of about 227 MeV. The effect of the width of $ρ$ and $f_0 (980)$ is also discussed. We associate this peak to the $ρ(1700)$ which has a mass of $1720 \pm 20$ MeV and a width of $250 \pm 100$ MeV.