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.

我们使用二体 Bethe-Salpeter 方程研究了一系列具有粲夸克贡献的四夸克状态的内部结构。因此，我们研究了具有隐藏魅力和夸克含量\(c\bar{c}q\bar{q}\)的类似charmonium状态，具有夸克含量\(cc\bar{q}\bar{q }\)和带有\(cc\bar{c}\bar{c}\)的全魅力状态。特别是我们研究了这些状态的波函数中介子 - 介子分量和双夸克 - 反二夸克分量之间的内部竞争。我们的结果表明\(\chi_{c1}(3872)\)和\(Z_c(3900)\)主要是\(D\bar{D}^*\)状态，并且最近发现的开-魅力状态\(T_{cc}^+\)由内部\(DD^*\)组件控制。在这两种情况下，双夸克分量都可以忽略不计。对于具有未知量子数的全魅力状态X (6900)，我们在\(0^+\)和\(1^+\)状态的激发光谱中识别候选者。此外，我们的框架用于为进一步的、尚未发现的开放和隐藏的魅力四夸克状态提供预测。