  Diquarks with $J^{P}=0^{\pm}$, $1^{\pm}$ containing a heavy (charm or bottom)
quark and a light quark are investigated using QCD Laplace sum rules. Masses
are determined using appropriately constructed gauge invariant correlation
functions, including for the first time next-to-leading order perturbative
contributions. The $J^P=0^+$ and $1^+$ charm-light diquark masses are
respectively found to be 1.86$\pm$0.05 GeV and 1.87$\pm$0.10 GeV, while those
of the $0^+$ and $1^+$ bottom-light diquarks are both determined to be
5.08$\pm$0.04 GeV. The sum rules derived for heavy-light diquarks with negative
parity are poorly behaved and do not permit unambiguous mass predictions, in
agreement with previous results for negative parity light diquarks. The scalar
and axial vector heavy-light diquark masses are degenerate within uncertainty,
as expected by heavy quark symmetry considerations. Furthermore, these mass
predictions are in good agreement with masses extracted in constituent diquark
models of the tetraquark candidates X(3872) and $Y_b(10890)$. Thus these
results provide QCD support for the interpretation of the X(3872) and
$Y_b(10890)$ as $J^{PC}=1^{++}$ tetraquark states composed of diquark clusters.
Further implications for tetraquarks among the heavy quarkonium-like XYZ states
are discussed.
