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

Abstract

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 $(250-500)\mathrm{MeV}$ 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 ${D^{\prime }}^{\ast }{\overline{D^{\prime }}}^{\ast }$, ${D^{\prime }}_s^{\ast }{\overline{D^{\prime }}}_s^{\ast }$, ${B^{\prime }}^{\ast }{\overline{B^{\prime }}}^{\ast }$ and ${B^{\prime }}_s^{\ast }{\overline{B^{\prime }}}_s^{\ast }$ molecular states maybe exist.

Comments: 19 pages, 36 figures, slight revision