We discuss the existence of states made of four heavy quarks in the context of potential models already used in the study of heavy mesons and baryons. We first consider the situation where the quarks have the same mass and interact through a two-body potential due to color-octet exchange. In this case, we show that for any reasonable confining potential there is no state below the threshold corresponding to the spontaneous dissociation into two mesons. We investigate in detail different possibilities of modifying this negative result. This concerns the effect of hyperfine corrections, the case of orbitally excited states, the case of unequal quark masses, and the use of the static potential derived from the bag model treated in the adiabatic approximation. -DO NARROW HEAVY MULTIQUARK STATES EXIST? 2371

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