Abstract
The question of whether there exist bound states of two heavy quarks $Q=(c,b)$ and antiquarks $\bar Q = (\bar c, \bar b)$, distinct from a pair of quark-antiquark mesons, has been debated for more than forty years. We suggest some means of producing and observing $Q_1 Q_2 \bar Q_3 \bar Q_4$ resonant states, concentrating on the $c c \bar c \bar c$ channel which is most easily produced and the $b b \bar b \bar b$ channel which has a better chance of being relatively narrow. We obtain $M_{(cc)(\bar c \bar c)} = 6,192 \pm 25$ MeV and $M_{(bb)(\bar b \bar b)} = 18,826 \pm 25$ MeV, for the charmed and bottom tetraquarks, respectively. Experimental search for these states in the relevant mass region is highly desirable.
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