On the nature of X(3960)

Abstract

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