# $0^{+}$ tetraquark states from improved QCD sum rules: delving into $X(5568)$

## TL;DR

This study uses improved QCD sum rules with higher-dimensional condensates to analyze the $X(5568)$ as a possible $0^{+}$ tetraquark, finding results consistent with experimental data and exploring different configurations.

## Contribution

The paper introduces an enhanced QCD sum rule approach including condensates up to dimension 12 to better analyze tetraquark states, especially the $X(5568)$.

## Key findings

- Scalar-scalar configuration mass: 5.57 GeV, matching experimental data.
- Axial-axial configuration mass: 5.77 GeV, also consistent with $X(5568)$.
- Pseudoscalar-pseudoscalar and vector-vector configurations have poor OPE convergence.

## Abstract

In order to investigate the possibility of the recently observed $X(5568)$ being a $0^{+}$ tetraquark state, we make an improvement to the study of the related various configuration states in the framework of the QCD sum rules. Particularly, to ensure the quality of the analysis, condensates up to dimension $12$ are included to inspect the convergence of operator product expansion (OPE) and improve the final results of the studied states. We note that some condensate contributions could play an important role on the OPE side. By releasing the rigid OPE convergence criterion, we arrive at the numerical value $5.57^{+0.35}_{-0.23}~\mbox{GeV}$ for the scalar-scalar diquark-antidiquark $0^{+}$ state, which agrees with the experimental data for the $X(5568)$ and could support its interpretation in terms of a $0^{+}$ tetraquark state with the scalar-scalar configuration. The corresponding result for the axial-axial current is calculated to be $5.77^{+0.44}_{-0.33}~\mbox{GeV}$, which is still consistent with the mass of $X(5568)$ in view of the uncertainty. The feasibility of $X(5568)$ being a tetraquark state with the axial-axial configuration therefore cannot be definitely excluded. For the pseudoscalar-pseudoscalar and the vector-vector cases, their unsatisfactory OPE convergence make it difficult to find reasonable work windows to extract the hadronic information.