Four-quark states with charm quarks in a two-body Bethe-Salpeter approach

Abstract

We study the internal structure of a range of four-quark states with charm quark contributions using a two-body Bethe-Salpeter equation. Thereby, we examine charmonium-like states with hidden charm and quark content $c\bar{c}q\bar{q}$, open-charm states with quark content $cc\bar{q}\bar{q}$ and all-charm states with $cc\bar{c}\bar{c}$. In particular we study the internal competition between meson-meson components and diquark-antidiquark components in the wave functions of these states. Our results indicate that the ${\chi }_{c1}(3872)$ and the $Z_c(3900)$ are predominantly $D{\bar{D}}^{\ast }$ states and that the recently discovered open-charm state $T_{cc}^{+}$ is dominated by an internal $D{D}^{\ast }$ component. In both cases the diquark components are negligible. For the all-charm state $X(6900)$ with as yet unknown quantum numbers we identify candidates in the excitation spectra of $0^{+}$ and $1^{+}$ states. Furthermore, our framework serves to provide predictions for further, yet undiscovered open and hidden charm four-quark states.

Comments: 9 pages, 4 figures; v2: minor changes, version accepted for EPJC