Is the exotic $X(5568)$ a bound state?

TL;DR

This study investigates the possibility of the exotic $X(5568)$ being a four-quark bound state using a chiral quark model, but finds no supporting evidence for such a structure.

Contribution

The paper applies Gaussian expansion method within the chiral quark model to analyze four-quark systems and assesses their potential as exotic states like $X(5568)$.

Findings

Diquark-antidiquark structures have too high energies to match $X(5568)$

No molecular or bound states are found for the studied tetraquark configurations

Results are consistent for both $usar{b}ar{d}$ and $usar{c}ar{d}$ systems

Abstract

Stimulated by the recent observation of the exotic $X(5568)$ state by D0 Collaboration, we study the four-quark system $us\bar{b}\bar{d}$ with quantum numbers $J^P=0^+$ in the framework of chiral quark model. Two structures, diquark-antidiquark and meson-meson, with all possible color configurations are investigated by using Gaussian expansion method. The results show that energies of the tetraquark states with diquark-antiquark structure are too high to the candidate of $X(5568)$, and no molecular structure can be formed in our calculations. The calculation is also extended to the four-quark system $us\bar{c}\bar{d}$ and the same results as that of $us\bar{b}\bar{d}$ are obtained.