  This paper is devoted to the study of exclusive charm and bottom aggregates
which are suitable, at least partially, for a non-relativistic description.
Starting from a simple choice of quarkonia and tetra-quark wave functions we
study their production cross sections, total widths and more interesting decay
properties.
  In particular, we compute the production cross sections of the ground state
scalar quarkonia getting results compatible with the values appearing in the
literature. We also compute the production cross sections of the lower energy
states of the charm and bottom tetra-quarks, their decay widths and the decay
rates in two $\mu\bar\mu$ pairs and in the $q\bar q\mu\bar\mu$ channel.
  Our results on the tetra-charm are consistent with the data published by the
LHCb Collaboration and those on the tetra-bottom show a reasonable agreement
with the indications published by the CMS Collaboration. Our cross section
analyses are based on interpolations based on the gluon-gluon luminosity grids
published by the NNPDF and CTEQ Collaborations. The hard amplitude calculations
are based on QCD in the tree approximation. We think that a careful improvement
of our method and a refinement of the experimental data after the foreseen
luminosity increase at the LHC will make possible valuable tests of QCD at the
intermediate energies.
