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^{\ast +}$$D_s^{\ast -}$. However, for the SU(3) symmetry the component $D_s^{\ast +}$$D_s^{\ast -}$ is coupled with the other components $D^{\ast 0}$${\bar{D}}^{\ast 0}$ and $D^{\ast +}$$D^{\ast -}$. Then we interpret the internal structure of the observed \emph{Y}(4140) state as a mixed state of pure molecule states $D^{\ast 0}$${\bar{D}}^{\ast 0}$, $D^{\ast +}$$D^{\ast -}$ and $D_s^{\ast +}$$D_s^{\ast -}$ 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.