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

Abstract

We perform a theoretical study on the $D\bar{D}K$ three body system, using the fixed center approximation to the Faddeev equations, considering the interaction between $D$ and $K$, $D$ and $\bar{D}$ from the chiral unitary approach. 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 the strong $DK$ interaction, where the scalar $D_{s0}^{\ast }(2317)$ meson is dynamically generated, a resonance structure shows up in the modulus squared of the three body $K$-$(D\bar{D}{)}_{X(3720)}$ scattering amplitude and supports that a $D\bar{D}K$ bound state can be formed. The result is in agreement with previous theoretical 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 mass about $4180$ MeV. It is expected that these theoretical results motivate its search in experimental measurements.

Comments: 6 pages, 5 figures. Typos fixed, more discussions added