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

TL;DR

This paper investigates heavy-quark tensor states as hadronic molecules using QCD sum rules, calculating their masses, decay widths, and dominant decay channels, revealing their instability and broad resonance nature.

Contribution

It introduces a QCD sum rule analysis of heavy-quark tensor states as hadronic molecules, providing mass estimates and decay properties for the first time.

Findings

Masses are approximately 15864 MeV and 9870 MeV.

Decay widths are about 120 MeV and 71 MeV.

Identifies dominant and subleading decay channels.

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 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} $ and $\Gamma[ \mathcal{M}_{\mathrm{T}}^{\mathrm{c}}]=(71 \pm 9)~ \mathrm{MeV} $ for the widths of these molecules characterize them as relatively broad structures.