  We discuss the effective field theory description of bound states composed of
a heavy baryon and antibaryon. This framework is a variation of the ones
already developed for heavy meson-antimeson states to describe the $X(3872)$ or
the $Z_c$ and $Z_b$ resonances. We consider the case of heavy baryons for which
the light quark pair is in S-wave and we explore how heavy quark spin symmetry
constrains the heavy baryon-antibaryon potential. The one pion exchange
potential mediates the low energy dynamics of this system. We determine the
relative importance of pion exchanges, in particular the tensor force. We find
that in general pion exchanges are probably non-perturbative for the $\Sigma_Q
\bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$
systems, while for the $\Xi_Q' \bar{\Xi}_Q'$, $\Xi_Q^* \bar{\Xi}_Q'$ and
$\Xi_Q^* \bar{\Xi}_Q^*$ cases they are perturbative If we assume that the
contact-range couplings of the effective field theory are saturated by the
exchange of vector mesons, we can estimate for which quantum numbers it is more
probable to find a heavy baryonium state. The most probable candidates to form
bound states are the isoscalar $\Lambda_Q \bar{\Lambda}_Q$, $\Sigma_Q
\bar{\Sigma}_Q$, $\Sigma_Q^* \bar{\Sigma}_Q$ and $\Sigma_Q^* \bar{\Sigma}_Q^*$
and the isovector $\Lambda_Q \bar{\Sigma}_Q$ and $\Lambda_Q \bar{\Sigma}_Q^*$
systems, both in the hidden-charm and hidden-bottom sectors. Their
doubly-charmed and -bottom counterparts ($\Lambda_Q {\Lambda}_Q$, $\Lambda_Q
{\Sigma}_Q^{(*)}$, $\Sigma_Q^{(*)} {\Sigma}_Q^{(*)}$) are also good candidates
for binding.
