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

This paper presents for the first time a precise measurement of the production properties of the $Z$-boson in the full phase space of the decay leptons. The measurement is based on proton-proton collision data collected by the ATLAS experiment in 2012 at $\sqrt{s} = 8$ TeV at the LHC and corresponding to an integrated luminosity of 20.2 $^{-1}$. This measurement, based on a total of 15.3 million $Z$-boson decays to electron and muon pairs, extends and improves a previous measurement of the full set of angular coefficients describing $Z$-boson decay. The double-differential cross-section distributions in $Z$-boson transverse momentum and rapidity are measured in the pole region, defined as $80 < m_Z < 100$ GeV, over the rapidity range $|y| < 3.6$. The total uncertainty of the normalised cross-section measurements in the bulk of the $p_T$ distribution is dominated by statistical uncertainties over the full range and increases as a function of rapidity from $0.5-1.0\%$ for $|y| < 2.0$ to $2-7\%$ at higher rapidities. The results for the transverse momentum rapidity-dependent distributions are compared to state-of-the-art QCD predictions, which combine in the best cases approximate N4LL resummation with N3LO fixed-order perturbative calculations. The differential rapidity distributions integrated 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-order QCD predictions using the most recent parton distribution functions.