Measurements of normalized differential crosssections of top-quark pair production are presented as a function of the top-quark, tt system and event-level kinematic observables in proton-proton collisions at a centre-of-mass energy of √ s = 8 TeV. The observables have been chosen to emphasize the tt production process and to be sensitive to effects of initial-and final-state radiation, to the different parton distribution functions, and to non-resonant processes and higher-order corrections. The dataset corresponds to an integrated luminosity of 20.3 fb −1 , recorded in 2012 with the ATLAS detector at the CERN Large Hadron Collider. Events are selected in the lepton+jets channel, requiring exactly one charged lepton and at least four jets with at least two of the jets tagged as originating from a b-quark. The measured spectra are corrected for detector effects and are compared to several Monte Carlo simulations. The results are in fair agreement with the predictions over a wide kinematic range. Nevertheless, most generators predict a harder top-quark transverse momentum distribution at high values than what is observed in the data. Predictions beyond NLO accuracy improve the agreement with data at high top-quark transverse momenta. Using the current settings and parton distribution functions, the rapidity distributions are not well modelled by any generator under consideration. However, the level of agreement is improved when more recent sets of parton distribution functions are used. IntroductionThe large top-quark pair production cross-section at the LHC allows detailed studies of the characteristics of tt production to be performed with respect to different kinematic variables, providing a unique opportunity to test the Standard Model (SM) at the TeV scale. Furthermore, effects beyond the SM can appear as modifications of tt differential distributions with respect to the SM predictions [1] which may not be detectable with an inclusive cross-section measurement. A precise measurement of the tt differential cross-section therefore has the potential to enhance the sensitivity to possible effects beyond the SM, as well as to clarify the ability of the theoretical calculations in describing the cross-section.The ATLAS [2][3][4] and CMS [5] experiments have published measurements of the tt differential cross-sections at a centre-of-mass energy √ s = 7 TeV in pp collisions, both in the full phase space using parton-level variables and in fiducial phase-space regions using observables constructed from 123 538 Page 2 of 39 Eur. Phys. J. C (2016) 76 :538 final-state particles (particle level); the CMS experiment also published measurements of the tt differential cross-sections with data taken at √ s = 8 TeV [6]. The results presented here represent the natural extension of the previous ATLAS measurements of the tt differential cross-sections to the √ s = 8 TeV dataset, and benefit from higher statistics and reduced detector uncertainties.In the SM, the top quark decays almost exclusively into a W boson and...

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