Possible ${\bar{D}}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ and ${\Xi }_{cc}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ molecules as superflavor partners of $T_{cc}$

Abstract

The doubly charmed tetraquark $T_{cc}$ has been reported by the LHCb experiment in 2022, and a lot of theoretical studies has been conducted. The small binding energy measured from $D^{\ast +}{D}^0$ threshold indicates that $T_{cc}$ is a $D{D}^{\ast }$ molecule. On the other hand, the superflavor symmetry, which relates heavy antiquarks to heavy diquarks, provides a useful framework for predicting the existence of partner exotic hadrons associated with $T_{cc}$. By replacing ${\bar{D}}^{(\ast )}$ with ${\Xi }_{cc}^{(\ast )}$ within this symmetry, ${\bar{D}}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ and ${\Xi }_{cc}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ are expected to form partner structures of $T_{cc}$. In this paper, we investigate bound and resonant states of ${\bar{D}}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ and ${\Xi }_{cc}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ based on the one boson exchange potential, where $\pi$, $\rho$, $\omega$ and $\sigma$ are considered as bosons. The cutoff parameter and the coupling constants for ${\bar{D}}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ and ${\Xi }_{cc}^{(\ast )}{\Xi }_{cc}^{(\ast )}$ are taken to be the same as those for $T_{cc}$ due to superflavor symmetry. We also discuss the $\sigma$ coupling constant, which is uncertain, dependence of these mass spectra. A lot of bound and resonant states with some quantum numbers are obtained for each $\sigma$ coupling constant, but these mass spectra depend on the $\sigma$ coupling constant significantly.

Comments: 11 pages, 6 figures, 8 tables