Investigation of the stability for fully-heavy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>c</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> tetraquark states

Abstract

We study the existence of fully-heavy hidden-flavor $bc\overline{b}\overline{c}$ tetraquark states with various ${J}^{PC}={0}^{\ifmmode\pm\else\textpm\fi{}+},{0}^{\ensuremath{-}\ensuremath{-}},{1}^{\ifmmode\pm\else\textpm\fi{}\ifmmode\pm\else\textpm\fi{}},{2}^{++}$, 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 $bc\overline{b}\overline{c}$ tetraquark states are about 12.2--12.4 GeV in both $[{\overline{\mathbf{3}}}_{\mathbf{c}}{]}_{bc}\ensuremath{\bigotimes}[{\mathbf{3}}_{\mathbf{c}}{]}_{\overline{b}\overline{c}}$ and $[{\mathbf{6}}_{\mathbf{c}}{]}_{bc}\ensuremath{\bigotimes}[{\overline{\mathbf{6}}}_{\mathbf{c}}{]}_{\overline{b}\overline{c}}$ color configuration channels. Except for two ${0}^{++}$ states, such results are below the thresholds ${T}_{{\ensuremath{\eta}}_{c}{\ensuremath{\eta}}_{b}}/{T}_{\mathrm{\ensuremath{\Upsilon}}\ensuremath{\psi}}$ and ${T}_{{B}_{c}{B}_{c}}$, implying that these $S$-wave positive parity $bc\overline{b}\overline{c}$ tetraquark states are probably stable against the strong interaction. For the $P$-wave negative parity $bc\overline{b}\overline{c}$ tetraquarks, their masses in the $[{\overline{\mathbf{3}}}_{\mathbf{c}}{]}_{bc}\ensuremath{\bigotimes}[{\mathbf{3}}_{\mathbf{c}}{]}_{\overline{b}\overline{c}}$ channel are around 12.9--13.2 GeV, while a bit higher in the $[{\mathbf{6}}_{\mathbf{c}}{]}_{bc}\ensuremath{\bigotimes}[{\overline{\mathbf{6}}}_{\mathbf{c}}{]}_{\overline{b}\overline{c}}$ channel. They can decay into the $c\overline{c}+b\overline{b}$ and $c\overline{b}+b\overline{c}$ final states via the spontaneous dissociation mechanism, including the $J/\ensuremath{\psi}\mathrm{\ensuremath{\Upsilon}}$, ${\ensuremath{\eta}}_{c}\mathrm{\ensuremath{\Upsilon}}$, $J/\ensuremath{\psi}{\ensuremath{\eta}}_{b}$, ${B}_{c}^{+}{B}_{c}^{\ensuremath{-}}$ channels.

Topics & Concepts