Investigation of the stability for fully-heavy $bc\bar{b}\bar{c}$ tetraquark states

Abstract

We study the existence of fully-heavy hidden-flavor $bc\bar{b}\bar{c}$ tetraquark states with various $J^{PC}=0^{\pm +},0^{--},1^{\pm \pm },2^{++}$, by using the moment QCD sum rule method augmented by fundamental inequalities. Using the moment sum rule analyses, our calculation shows that the masses for the S-wave positive parity $bc\bar{b}\bar{c}$ tetraquark states are about $12.2-12.4$ GeV in both $[{\bar{3}}_{\mathbf{c}}{]}_{bc}\otimes [3_{\mathbf{c}}{]}_{\bar{b}\bar{c}}$ and $[6_{\mathbf{c}}{]}_{bc}\otimes [{\bar{6}}_{\mathbf{c}}{]}_{\bar{b}\bar{c}}$ color configuration channels. Except for two $0^{++}$ states, such results are below the thresholds $T_{{\eta }_c{\eta }_b}/T_{{\rm Y}\psi }$ and $T_{B_c{B}_c}$, implying that these S-wave positive parity $bc\bar{b}\bar{c}$ tetraquark states are probably stable against the strong interaction. For the P-wave negative parity $bc\bar{b}\bar{c}$ tetraquarks, their masses in the $[{\bar{3}}_{\mathbf{c}}{]}_{bc}\otimes [3_{\mathbf{c}}{]}_{\bar{b}\bar{c}}$ channel are around $12.9-13.2$ GeV, while a bit higher in the $[6_{\mathbf{c}}{]}_{bc}\otimes [{\bar{6}}_{\mathbf{c}}{]}_{\bar{b}\bar{c}}$ channel. They can decay into the $c\bar{c}+b\bar{b}$ and $c\bar{b}+b\bar{c}$ final states via the spontaneous dissociation mechanism, including the $J/\psi {\rm Y}$, ${\eta }_c{\rm Y}$, $J/\psi {\eta }_b$, $B_c^{+}{B}_c^{-}$ channels.

Comments: 19 pages, 3 figures. Version appears in PRD