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This paper presents for the first time a precise measurement of theproduction properties of the Z boson in the full phase space of the decayleptons. The measurement is obtained from proton-proton collision datacollected by the ATLAS experiment in 2012 at $\sqrt s$ = 8 TeV at the LHC andcorresponding to an integrated luminosity of 20.2 fb$^{-1}$. The results, basedon a total of 15.3 million Z-boson decays to electron and muon pairs, extendand improve a previous measurement of the full set of angular coefficientsdescribing Z-boson decay. The double-differential cross-section distributionsin Z-boson transverse momentum p$_T$ and rapidity y are measured in the poleregion, defined as 80 $<$ m $<$ 100 GeV, over the range $|y| <$ 3.6. The totaluncertainty of the normalised cross-section measurements in the peak region ofthe p$_T$ distribution is dominated by statistical uncertainties over the fullrange and increases as a function of rapidity from 0.5-1.0% for $|y| <$ 2.0 to2-7% at higher rapidities. The results for the rapidity-dependent transversemomentum distributions are compared to state-of-the-art QCD predictions, whichcombine in the best cases approximate N$^4$LL resummation with N$^3$LOfixed-order perturbative calculations. The differential rapidity distributionsintegrated over p$_T$ are even more precise, with accuracies from 0.2-0.3% for$|y| <$ 2.0 to 0.4-0.9% at higher rapidities, and are compared to fixed-orderQCD predictions using the most recent parton distribution functions. Theagreement between data and predictions is quite good in most cases.

A precise measurement of the Z-boson double-differential transverse  momentum and rapidity distributions in the full phase space of the decay  leptons with the ATLAS experiment at $\sqrt s$ = 8 TeV