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

Parametrically narrow tetraquark states containing one heavy quark and one heavy antiquark