Molecular states $J/\psi B_{c}^{+}$ and $\eta_{c}B_{c}^{\ast +} $

TL;DR

This paper predicts the properties of hadronic molecules composed of $J/\psi B_c^+$ and $\eta_c B_c^{*+}$ using QCD sum rules, providing mass and decay width estimates relevant for experimental searches.

Contribution

It offers the first detailed QCD sum rule analysis of these specific molecular states, including mass predictions and decay mechanisms.

Findings

Predicted mass of $J/\psi B_c^+$ molecule: $(9740 \pm 70)$ MeV.

Computed decay width of the molecule: $(121 \pm 17)$ MeV.

Identified dominant and subdominant decay channels for the molecule.

Abstract

Hadronic molecules $\mathfrak{M}=J/\psi B_{c}^{+}$ and $\widetilde{\mathfrak{ \ M}}=\eta _{c}B_{c}^{\ast +}$ 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 coinciding within accuracy of the sum rule method. Therefore, we concentrate on the molecule $J/\psi B_{c}^{+}$ and explore features of this state in a detailed form. 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 $\mathfrak{M} \to J/\psi B_{c}^{+}$ and $\mathfrak{M} \to \eta _{c}B_{c}^{\ast +}$. Annihilation of $ \overline{c}c$ quarks triggers subdominant processes with various final-state $B$ and $D$ mesons: Six of such channels are considered in this work. The partial widths all of decays are computed using the three-point sum rule approach. The width $\Gamma[ \mathfrak{M}]=(121 \pm 17)~ \mathrm{MeV }$ of the hadronic axial-vector molecule $\mathfrak{M}$, as well as its mass provide valuable information for running and future experiments.