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

Abstract

We perform a theoretical study on the Dbar{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 Dbar{D}, where a scalar meson X(3720) could be formed. Thanks to the strong DK interaction, where the scalar D^*_{s0}(2317) meson is dynamically generated, a resonance structure shows up in the modulus squared of the three body K-(Dbar{D})_{X(3720)} scattering amplitude and supports that a Dbar{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_{cbar{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.