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

Abstract

AbstractWe 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 $$c\bar{c}q\bar{q}$$ c c ¯ q q ¯ , open-charm states with quark content $$cc\bar{q}\bar{q}$$ c c q ¯ q ¯ and all-charm states with $$cc\bar{c}\bar{c}$$ c c c ¯ 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 $$\chi _{c1}(3872)$$ χ c 1 ( 3872 ) and the $$Z_c(3900)$$ Z c ( 3900 ) are predominantly $$D\bar{D}^*$$ D D ¯ ∗ states and that the recently discovered open-charm state $$T_{cc}^+$$ T cc + is dominated by an internal $$DD^*$$ D D ∗ 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 $$0^+$$ 0 + and $$1^+$$ 1 + states. Furthermore, our framework serves to provide predictions for further, yet undiscovered open and hidden charm four-quark states.