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We perform a theoretical study on the $D\bar{D}K$ three body system, usingthe fixed center approximation to the Faddeev equations, considering theinteraction between $D$ and $K$, $D$ and $\bar{D}$ from the chiral unitaryapproach. We assume the scattering of $K$ meson on a clusterized system$D\bar{D}$, where a scalar meson $X(3720)$ could be formed. Thanks to thestrong $DK$ interaction, where the scalar $D^*_{s0}(2317)$ meson is dynamicallygenerated, a resonance structure shows up in the modulus squared of the threebody $K$-$(D\bar{D})_{X(3720)}$ scattering amplitude and supports that a$D\bar{D}K$ bound state can be formed. The result is in agreement with previoustheoretical studies, which claim a new excited hidden charm $K$ meson,$K_{c\bar{c}}(4180)$ with quantum numbers $I(J^P) = \frac{1}{2}(0^-)$ and massabout $4180$ MeV. It is expected that these theoretical results motivate itssearch in experimental measurements.

Faddeev fixed-center approximation to the $D\bar{D}K$ system and the hidden charm $K_{c\bar{c}}(4180)$ state