Symmetry has imposed very strong constraints on the internal structure of q
uantum mechanical system. In particular, whether a state can access a given
outgoing channel is constrained by symmetry. For the dipositroniums, the m
ost important channel is the Ps-Ps channel. However, based on symmetry cons
ideration it was found that only a few excited states are allowed to access
the Ps-Ps channel, thereby at least the existence of two higher L = 0 boun
d states (higher than the Ps-Ps threshold) has been affirmed.