Tensor states $\Upsilon B_{c}^{\ast -}$ and $J/\psi B_{c}^{\ast +}$

Abstract

Tensor states $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}}=\Upsilon B_{c}^{\ast -}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}=J/\psi B_{c}^{\ast +}$ are explored using techniques of QCD sum rule method. These hadronic molecules, composed of only heavy quarks, have asymmetric quark contents $bb\overline{b} \overline{c}$ and $cc\overline{c}\overline{b}$, respectively. The masses $ m=(15864 \pm 85)~\mathrm{MeV}$ and $\widetilde{m}=(9870 \pm 82)~\mathrm{MeV} $ prove that these structures are unstable against dissociations to constituent mesons. Full widths of molecules $\mathcal{M}_{\mathrm{T}}^{ \mathrm{b}}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}$ are calculated by considering their dominant and subleading decay channels. The subleading channels are processes generated by annihilations of $\overline{b}b$ and $ \overline{c}c$ quarks. For the molecule $\mathcal{M}_{\mathrm{T}}^{\mathrm{b} }$ dominant decays are $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}} \to \Upsilon B_{c}^{\ast -}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}} \to \eta_b B_{c}^{-}$, whereas subleading channels are transformations to $\mathcal{M} _{ \mathrm{T}}^{\mathrm{b}}\rightarrow B^{(\ast )-}\overline{D}^{(\ast )0}$ and $\overline{B}_{(s)}^{(\ast )0}D_{(s)}^{(\ast )-}$ mesons. In the lower limit ($\mathrm{l.l.}$) of the mass $m=15779~\mathrm{MeV}$ for $\mathcal{M}_{ \mathrm{T}}^{\mathrm{b}}$ decay to $\Upsilon B_{c}^{\ast -}$ mesons is forbidden. In the case of $\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}$ we explore decays to $J/\psi B_{c}^{\ast +}$, $\eta_{c}B_{c}^{+}$, $B^{(\ast)+}D^{(\ast )0}$ and $B_{(s)}^{(\ast )0}D_{(s)}^{(\ast )+}$ mesons. Predictions $\Gamma[ \mathcal{M} _{\mathrm{T}}^{\mathrm{b}}]=120^{+17}_{-12}~ \mathrm{MeV}$, $ \Gamma[\mathcal{M}_{\mathrm{T}}^{\mathrm{b}}]_{\mathrm{l.l.}}=(65 \pm 7)~ \mathrm{MeV}$ and ...