  Constituent mass predictions for axial vector (i.e., $J^P=1^+$) $cc$ and $bb$
colour antitriplet diquarks are generated using QCD Laplace sum-rules. We
calculate the diquark correlator within the operator product expansion to NLO,
including terms proportional to the four- and six-dimensional gluon and
six-dimensional quark condensates. The sum-rules analyses stabilize, and we
find that the mass of the $cc$ diquark is 3.51~GeV and the mass of the $bb$
diquark is 8.67~GeV. Using these diquark masses as inputs, we calculate several
tetraquark masses within the Type-II diquark-antidiquark tetraquark model.
