  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 f_0(600). Our results furthermore suggest
the presence of a potentially narrow all-charm tetraquark in the mass region
5-6 GeV.
