  This paper focuses on tetraquarks containing one heavy quark and one heavy
antiquark in the formal limit where the heavy quark masses go to infinity. It
extends the theoretical framework developed for tetraquark containing two heavy
quarks based on semi-classical analysis and the Born-Oppenheimer approximation.
It is shown that for sufficiently small light quark masses, parametrically
narrow $q\bar{q}'Q\bar{Q}$ tetraquarks must exist in the formal limit of
arbitrarily large heavy quark masses. The analysis is model-independent; it
requires no assumptions about the structure of the state or the mechanism of
its decay beyond what can be deduced directly from QCD. The formal analysis
here is only directly applicable to tetraquarks with large angular momentum and
hence does not directly apply to experimentally observed tetraquark candidates.
We also discuss the condition needed for a version of the analysis to apply for
low angular momenta states. Whether this condition holds can be explored via
lattice calculations. Current lattice calculations suggest that the condition
is not met. If these preliminary calculations are confirmed, there are strong
implications for the nature of the observed tetraquark resonances containing
$\bar{c}c$ or $\bar{b}b$ pairs. It raises the possibility that the observed
tetraquarks exist and are narrow not because the charm and bottom quarks are
extremely heavy, but because they are sufficiently light.
