Molecular states $J/ψB_{c}^{+}$ and $η_{c}B_{c}^{\ast +} $

TL;DR

The study applies QCD sum rules to the axial-vector fully heavy molecular states $\mathfrak{M}=J/\psi B_{c}^{+}$ and $\widetilde{\mathfrak{M}}=\eta_{c}B_{c}^{\ast +}$, estimating their masses and current couplings and finding $m=(9740 \pm 70)~\mathrm{MeV}$ with closely related values for the partner state. Masses being above two-meson thresholds imply these are resonances that readily decay, which the authors quantify via dominant decays $\mathfrak{M}\rightarrow J/\psi B_{c}^{+}$ and $\mathfrak{M}\rightarrow \eta_{c}B_{c}^{\ast +}$ with partial widths $\Gamma=(40.6\pm12.4)$ MeV and $36.8\pm9.5$ MeV, respectively, and several subdominant channels analyzed with three-point SR giving total width $\Gamma[\mathfrak{M}]=(121\pm17)$ MeV. The work also explores subdominant and strange-mchannel decays, showing that the overall width emerges from both fall-apart and annihilation mechanisms, and concludes these states are broad, resonant structures rather than bound states. The results provide precise SR-based predictions to guide current and future experiments and offer context for comparisons with diquark–antidiquark pictures in the fully heavy sector.

Abstract

Hadronic molecules $\mathfrak{M}=J/ψB_{c}^{+}$ and $\widetilde{\mathfrak{ M}}=η_{c}B_{c}^{\ast +}$ are investigated in the framework of QCD sum rule method. These particles with spin-parities $J^{\mathrm{P}}=1^+$ have the quark contents $cc \overline{c}\overline{b}$. We compute their masses and current couplings and find that they are numerically very close to each other. Because it is difficult to distinguish reliably the molecules $J/ψB_{c}^{+}$ and $J/ψB_{c}^{+}$, we treat them as identical structures, and consider in details the state $\mathfrak{M}$. Our prediction $m=(9740 \pm 70)~\mathrm{MeV}$ for its mass means that $\mathfrak{M}$ easily decays to pairs of ordinary mesons through strong interactions. There are two mechanisms responsible for transformations of $\mathfrak{M}$ to conventional mesons. The fall-apart mechanism generates the dominant decay channels $ \mathfrak{M} \to J/ψB_{c}^{+}$ and $\mathfrak{M} \to η_{c}B_{c}^{\ast +}$. Annihilation of $\overline{c}c$ quarks triggers subdominant processes with various final-state $B$ and $D$ mesons: Six of such channels are explored in this work. The partial widths of all decays are computed using the three-point sum rule approach. The width $Γ[ \mathfrak{M}]=(121 \pm 17)~ \mathrm{MeV}$ of the hadronic axial-vector molecule $\mathfrak{M}$, as well as its mass are valuable for running and future experiments.

Figures (4)

• Figure 1: $\mathrm{PC}$ as a function of the Borel parameter $M^{2}$ at fixed $s_{0}$. The star shows the point $M^{2}=9~\mathrm{GeV}^{2}$ and $s_{0}=110~\mathrm{GeV}^{2}$.
• Figure 2: Dependence of $m$ on the parameters $M^{2}$ (left panel), and $s_0$ (right panel).
• Figure 3: SR data and fit functions $\mathcal{Z}_1 (Q^{2})$ (solid curve) and $\mathcal{Z}_2 (Q^{2})$ (dashed line). The triangle and circle denote the points $Q^{2}=-m_{J/\psi}^{2}$ and $Q^{2}=-m_{\eta_c}^2$, respectively.
• Figure 4: SR data for $G_1(Q^{2})$ and $G_{2}(Q^2)$, and extrapolating functions $\widehat{\mathcal{Z}}_1(Q^{2})$ (solid curve), and $\widehat{\mathcal{Z}}_2(Q^{2})$ (dot-dashed curve). The points $Q^{2}=-m_{\overline{D}_{s}^{\ast}}^{2}$ and $Q^{2}=-m_{D_{s}}^{2}$ are denoted by the rectangle and triangle, respectively.