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

Abstract

Abstract We perform a theoretical study on the $$D\bar{D}K$$ D D ¯ K three body system, using the fixed center approximation to the Faddeev equations, considering the interaction between D and K, D and $$\bar{D}$$ D ¯ from the chiral unitary approach. We assume the scattering of K meson on a clusterized system $$D\bar{D}$$ D D ¯ , where a scalar meson X(3720) could be formed. Thanks to the strong DK interaction, where the scalar $$D^*_{s0}(2317)$$ D s 0 ∗ ( 2317 ) meson is dynamically generated, a resonance structure shows up in the modulus squared of the three body K- $$(D\bar{D})_{X(3720)}$$ ( D D ¯ ) X ( 3720 ) scattering amplitude and supports that a $$D\bar{D}K$$ D 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, $$K_{c\bar{c}}(4180)$$ K c c ¯ ( 4180 ) with quantum numbers $$I(J^P) = \frac{1}{2}(0^-)$$ I ( J P ) = 1 2 ( 0 - ) and mass about 4180 MeV. It is expected that these theoretical results motivate its search in experimental measurements.