Tetraquark bound states in a Bethe–Salpeter approach

We determine the mass of tetraquark bound states from a coupled system of covariant Bethe–Salpeter equations. Similar in spirit to the quark–diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark–gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion–pion constituents. Both results are in agreement with a meson molecule picture for the f0(600). Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5–6 GeV.