We show that the $K_2^{*}(1430)$, $K_3^{*}(1780)$, $K_4^{*}(2045)$, $K_5^{*}(2380)$, and a not-yet-discovered $K_6^{*}$ resonance are basically molecules made of an increasing number of $\rho (770)$ and one $K^{*}(892)$ mesons. The idea relies on the fact that the vector-vector interaction in the $s$ wave with spins aligned is very strong for both $\rho \rho$ and $K^{*}\rho$. We extend a recent work, where several resonances showed up as multi-$\rho (770)$ molecules, to the strange sector including the $K^{*}(892)$ into the system. The resonant structures show up in the multibody scattering amplitudes, which are evaluated in terms of the unitary two-body vector-vector scattering amplitudes by using the fixed center approximation to the Faddeev equations.

• Received 4 October 2010

DOI:https://doi.org/10.1103/PhysRevD.82.094017