Analysis of the Y(4140) with QCD sum rules

In this article, we assume that there exists a scalar $D_s^\ast {\bar D}_s^\ast$ molecular state in the $J/\psi \phi$ invariant mass distribution, and study its mass using the QCD sum rules. The predictions depend heavily on the two criteria (pole dominance and convergence of the operator product expansion) of the QCD sum rules. The value of the mass is about $M_{D_s^\ast {\bar D}_s^\ast}=(4.43\pm0.16) \rm{GeV}$, which is inconsistent with the experimental data. The $D_s^\ast {\bar D}_s^\ast$ is probably a virtual state and not related to the meson Y(4140). Other possibility, such as a hybrid charmonium is not excluded.