Tensor states $ΥB_{c}^{\ast -}$ and $J/ψB_{c}^{\ast +}$

TL;DR

This paper applies QCD sum rules to fully heavy tensor hadronic molecules with asymmetric quark content, $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}}=ΥB_{c}^{\ast -}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}=J/ψB_{c}^{\ast +}$, extracting their masses $m$ and $\widetilde{m}$ and current couplings $\Lambda$ and $\widetilde{\Lambda}$. It subsequently computes the full decay widths by evaluating leading and subleading strong decay channels via three-point sum rules, using extrapolation functions to obtain on-shell couplings. The results show $m=15864\pm85$ MeV and $\widetilde{m}=9870\pm82$ MeV, with total widths $\Gamma[\mathcal{M}_{\mathrm{T}}^{\mathrm{b}}]=120_{-12}^{+17}$ MeV and $\Gamma[\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}]=(71\pm9)$ MeV, indicating relatively broad resonances that are unstable against dissociation to constituent mesons or to heavy-muon-poor final states via annihilation channels. These findings provide quantitative predictions for future experimental searches and complement prior analyses of scalar and axial-vector fully heavy molecules, advancing understanding of the spectroscopy and decay behavior of asymmetric heavy tetraquarks.

Abstract

Tensor states $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}}=ΥB_{c}^{\ast -}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{c}}=J/ψB_{c}^{\ast +}$ 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 $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}} \to ΥB_{c}^{\ast -}$ and $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}} \to η_b B_{c}^{-}$, 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 $J/ψB_{c}^{\ast +}$, $η_{c}B_{c}^{+}$, $B^{(\ast)+}D^{(\ast )0}$ and $ B_{(s)}^{(\ast )0}D_{(s)}^{(\ast )+}$ mesons. Predictions $Γ[\mathcal{M} _{\mathrm{T}}^{\mathrm{b}}]=120^{+17}_{-12}~ \mathrm{MeV} $ and $Γ[ \mathcal{M}_{\mathrm{T}}^{\mathrm{c}}]=(71 \pm 9)~ \mathrm{MeV} $ for the widths of these molecules characterize them as relatively broad structures.

Figures (5)

• Figure 1: Dependence of $\mathrm{PC}$ on $M^{2}$ for different $s_{0}$. The constant line shows the border $\mathrm{PC}=0.5$. The star marks the point $M^{2}=18.5~\mathrm{GeV}^{2}$ and $s_{0}=282.5~\mathrm{GeV}^{2}$.
• Figure 2: Mass $m$ of $\mathcal{M}_{\mathrm{T}}^{\mathrm{b}}$ as a function of the Borel $M^{2}$ (left), and continuum threshold $s_0$ parameters (right).
• Figure 3: Dependence of the mass $\widetilde{m}$ on the Borel $M^{2}$ (left), and continuum threshold $s_0$ parameters (right).
• Figure 4: QCD data and fit function for $g_{1}(Q^{2})$. The diamond shows the point $Q^{2}=-m_{B_{c}^{\ast}}^{2}$ where $g_{1}$ has been evaluated.
• Figure 5: SR data and fit functions for the form factors $g_{4}(Q^{2})$ (solid line) and $g_{6}(Q^{2})$ (dot-dashed line). The diamond and star mark fix the points $Q^{2}=-m_{D^{0}}^{2}$ and $Q^{2}=-m_{D_{s}^{0}}^{2}$, respectively.