  For very heavy quarks $Q$, relations derived from heavy-quark symmetry
predict the existence of novel narrow doubly heavy tetraquark states of the
form $Q_iQ_j \bar q_k \bar q_l$ (subscripts label flavors), where $q$
designates a light quark. By evaluating finite-mass corrections, we predict
that double-beauty states composed of $bb\bar u \bar d$, $bb\bar u \bar s$, and
$bb\bar d \bar s$ will be stable against strong decays, whereas the
double-charm states $cc \bar q_k \bar q_l$, mixed beauty+charm states $bc \bar
q_k \bar q_l$, and heavier $bb \bar q_k \bar q_l$ states will dissociate into
pairs of heavy-light mesons. Observation of a new double-beauty state through
its weak decays would establish the existence of tetraquarks and illuminate the
role of heavy color-antitriplet diquarks as hadron constituents.
