Analysis of the Y(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar ${D}^\ast {\bar {D}}^\ast$, ${D}_s^\ast {\bar {D}}_s^\ast$, ${B}^\ast {\bar {B}}^\ast$ and ${B}_s^\ast {\bar {B}}_s^\ast$ molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about $(250-500) \rm{MeV}$ above the corresponding ${D}^\ast -{\bar {D}}^\ast$, ${D}_s^\ast -{\bar {D}}_s^\ast$, ${B}^\ast -{\bar {B}}^\ast$ and ${B}_s^\ast -{\bar {B}}_s^\ast$ thresholds, the Y(4140) is unlikely a scalar ${D}_s^\ast {\bar {D}}_s^\ast$ molecular state. The scalar $D^\ast {\bar D}^\ast$, $D_s^\ast {\bar D}_s^\ast$, $B^\ast {\bar B}^\ast$ and $B_s^\ast {\bar B}_s^\ast$ molecular states maybe not exist, while the scalar ${D'}^\ast {\bar {D'}}^\ast$, ${D'}_s^\ast {\bar {D'}}_s^\ast$, ${B'}^\ast {\bar {B'}}^\ast$ and ${B'}_s^\ast {\bar {B'}}_s^\ast$ molecular states maybe exist.