Scalar molecules $\eta _{b}B_{c}^{-}$ and $\eta _{c}B_{c}^{+} $ with asymmetric quark contents

TL;DR

This paper investigates the properties and decay modes of scalar molecules with asymmetric quark contents using QCD sum rule methods, providing mass, width estimates, and decay channels to aid experimental searches.

Contribution

It introduces a novel application of QCD sum rules to calculate masses, widths, and decay channels of asymmetric scalar molecules, which are unstable and transform into meson pairs.

Findings

Mass of $ ext{M}_b$ is $(15728 ext{ MeV} ext{ with } ext{width} ext{ } 93 ext{ MeV}$.

Mass of $ ext{M}_c$ is $(9712 ext{ MeV} ext{ with } ext{width} ext{ } 70 ext{ MeV}$.

Main decay channels identified for both molecules.

Abstract

The hadronic scalar molecules $\mathcal{M}_{b}$ and $\mathcal{M}_{c}$ with asymmetric quark contents $bb \overline{b}\overline{c}$ and $cc \overline{c} \overline{b}$ are explored by means of the QCD sum rule method. Their masses and current couplings are calculated using the two-point sum rule approach. The obtained results show that they are strong-interaction unstable particles and transform to ordinary mesons' pairs. The molecule $\mathcal{M} _{b}$ dissociates through the process $\mathcal{M}_{\mathrm{b}}\to \eta _{b}B_{c}^{-}$. The decays $\mathcal{M}_{\mathrm{c}}\rightarrow \eta _{c}B_{c}^{+}$ and $J/\psi B_{c}^{\ast +}$ are dominant modes for the molecule $\mathcal{M}_{c}$. The full decay widths of the molecules $\mathcal{ \ \ M}_{b}$ and $\mathcal{M}_{c}$ are estimated using these decay channels, as well as ones generated by the annihilation of $b\overline{b}$ and $c \overline{c}$ quarks in $\mathcal{M}_{b}$ and $\mathcal{M}_{c}$, respectively. The QCD three-point sum rule method is employed to find partial widths all of these channels. This approach is required to evaluate the strong couplings at the molecule-meson-meson vertices under consideration. The mass $m=(15728 \pm 90)~\mathrm{MeV}$ and width $\Gamma[ \mathcal{M}_b] =(93 \pm 17)~ \mathrm{MeV}$ of the molecule $\mathcal{M}_{b}$ , and $\widetilde{m}=(9712 \pm 72)~\mathrm{MeV}$ and $\Gamma[\mathcal{M}_c] =(70 \pm 10)~ \mathrm{MeV}$ in the case of $\mathcal{M}_{c} $ offer valuable guidance for experimental searches at existing facilities.