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

TL;DR

This paper investigates the internal structure of various four-quark states with charm quarks using a two-body Bethe-Salpeter approach, revealing dominant meson-meson components in known states and predicting new states.

Contribution

It introduces a novel application of the two-body Bethe-Salpeter equation to analyze four-quark states with charm quarks, highlighting the internal composition and providing predictions for undiscovered states.

Findings

$ ext{X}(6900)$ identified as a candidate in $0^+$ and $1^+$ spectra.

$ ext{Z}_c(3900)$ and $ ext{X}(3872)$ are mainly $Dar D^*$ states.

Open-charm state $T_{cc}^+$ dominated by $DD^*$ component.

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 $D\bar D^*$ states and that the recently discovered open-charm state $T_{cc}^+$ is dominated by an internal $DD^*$ 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.