Scalar Triple-Heavy Tetraquark States With Quark Content $cc\bar{c}\bar{s}$

TL;DR

This study investigates scalar triple-heavy tetraquark states with quark content $cc\bar{c}\bar{s}$ using QCD sum rules, providing mass predictions and analyzing molecular and compact configurations.

Contribution

The paper introduces specific interpolating currents for these tetraquark states and derives sum rules to predict their masses and couplings, a novel application for this quark content.

Findings

Mass of $\eta_c D_s$ molecular state: ~4.94 GeV

Masses of compact tetraquark states: ~5.07 GeV

Quantitative estimates of current coupling constants.

Abstract

In this paper, we study the scalar triple-heavy tetraquark states with quark content $cc\bar{c}\bar{s}$, $\eta_{c}D_{s}$ molecular state and $[cc]_{A(T)}[\bar{c}\bar{s}]_{A(T)}$ compact tetraquark states, by the QCD sum rule method. First, we construct the needed interpolating currents, $J^{M}(x)$, $J^{T_{1}}(x)$, and $J^{T_{2}}(x)$. Then, we derive the sum rules for the masses and the current coupling constants. Finally, we numerically analyze these sum rules, and find $m_{M}=4.9392^{+0.0851}_{-0.0817}~\mbox{GeV}$, and $\lambda_{M}=2.8857^{+0.5729}_{-0.4928}\times10^{-2}~\mbox{GeV}^{5}$ for the mass and the current coupling constant of the $\eta_{c}D_{s}$ molecular state, $m_{T_{1}}=5.0774^{+0.0708}_{-0.0641}~\mbox{GeV}$, and $\lambda_{T_{1}}=1.0436^{+0.1862}_{-0.1573}\times10^{-1}~\mbox{GeV}^{5}$ for the mass and the current coupling constant of the $[cc]_{A}[\bar{c}\bar{s}]_{A}$ compact tetraquark state, $m_{T_{2}}=5.0679^{+0.0839}_{-0.0721}~\mbox{GeV}$, and $\lambda_{T_{2}}=2.0316^{+0.4119}_{-0.3119}\times10^{-1}~\mbox{GeV}^{5}$ for the mass and the current coupling constant of the $[cc]_{T}[\bar{c}\bar{s}]_{T}$ compact tetraquark state.