Exploring the nature of ${\eta }_1(1855)$ and it's partner in a chiral quark model

Inspired by the recent experimental discoveries of $X(3872)$ ($c\bar{q}$-$q\bar{c}$) and $T_{cc}$ ($c\bar{q}$-$c\bar{q}$), we systematically study two four-quark systems: the $K{K}_1$ ($q\bar{s}$-$q\bar{s}$) system and the $K{\bar{K}}_1$ ($q\bar{s}$-$s\bar{q}$) system, which is a candidate for the recently observed ${\eta }_1(1855)$. Within the framework of an accurate few-body calculation method (GEM), we employ the chiral quark model to simultaneously consider the molecular and diquark structures of these two multiquark systems and include their channel coupling effects. Our results show that the $K{\bar{K}}_1$ system remains a scattering state. On the other hand, due to the presence of a good-diquark structure in the $K{K}_1$ system, we obtain a bound state in the coupled-channel calculation. The primary contribution to the binding energy comes from the exchange of $\pi$-meson and $\sigma$-meson. The inter-quark distance indicates that it is a compact four-quark structure.