  The transverse momentum distribution of massive neutral vector bosons can be
measured to high accuracy at hadron colliders. The transverse momentum is
caused by a partonic recoil, and is determined by QCD dynamics. We compute the
single and double-differential transverse momentum distributions for fully
inclusive $Z/\gamma^*$ production including leptonic decay to
next-to-next-to-leading order (NNLO) in perturbative QCD. We also compute the
same distributions normalised to the cross sections for inclusive $Z/\gamma^*$
production, i.e. integrated over the transverse momentum of the lepton pair. We
compare our predictions for the fiducial cross sections to the 8 TeV data set
from the ATLAS and CMS collaborations, which both observed a tension between
data and NLO theory predictions, using the experimental cuts and binning. We
find that the inclusion of the NNLO QCD effects does not fully resolve the
tension with the data for the unnormalised $p^Z_T$ distribution. However, we
observe that normalising the NNLO $Z$-boson transverse momentum distribution by
the NNLO Drell-Yan cross section substantially improves the agreement between
experimental data and theory, and opens the way for precision QCD studies of
this observable.
