Mass of \emph{Y}(4140) in Bethe-Salpeter equation for quarks

Abstract

Using the general form of the Bethe-Salpeter wave functions for the bound states consisting of two vector fields given in our previous work, we investigate the molecular state composed of $D^{*+}_s$$D^{*-}_s$. However, for the SU(3) symmetry the component $D^{*+}_s$$D^{*-}_s$ is coupled with the other components $D^{*0}$$\bar{D}^{*0}$ and $D^{*+}$$D^{*-}$. Then we interpret the internal structure of the observed \emph{Y}(4140) state as a mixed state of pure molecule states $D^{*0}$$\bar{D}^{*0}$, $D^{*+}$$D^{*-}$ and $D^{*+}_s$$D^{*-}_s$ with quantum numbers $J^P=0^+$. In this paper, the operator product expansion is used to introduce the nonperturbative contribution from the vacuum condensates into the interaction between two heavy mesons. The calculated mass of \emph{Y}(4140) is consistent with the experimental value, and we conclude that it is a more reasonable scenario to explain the structure of Y (4140) as a mixture of pure molecule states.