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 cc¯ qq¯ , open-charm states with quark content ccq¯ q¯ and all-charm states with ccc¯ 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 χc1(3872) and the Zc(3900) are predominantly DD¯ ∗ states and that the recently discovered open-charm state Tcc+ 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.