On the nature of X(3960)

Abstract A near-threshold enhancement in the $$D^{+}_{s}D^{-}_{s}$$ D s + D s - system, dubbed as X(3960), is observed by the LHCb collaboration recently. A combined analysis on $$\chi _{c0}(3930)~(\rightarrow D^+ D^-)$$ χ c 0 ( 3930 ) ( → D + D - ) , $$X(3960)~(\rightarrow D^{+}_{s}D^{-}_{s})$$ X ( 3960 ) ( → D s + D s - ) , and $$X(3915)~(\rightarrow J/\psi \omega )$$ X ( 3915 ) ( → J / ψ ω ) is performed using both a K-matrix approach of $$D_{(s)}\bar{D}_{(s)}$$ D ( s ) D ¯ ( s ) four-point contact interactions and a model of Flatté-like parameterizations. The use of the pole counting rule and spectral density function sum rule indicate, under current statistics, that this $$D^{+}_{s}D^{-}_{s}$$ D s + D s - near-threshold state has probably the mixed nature of a $$c\bar{c}$$ c c ¯ confining state and $$D^{+}_{s}D^{-}_{s}$$ D s + D s - continuum