Studies of the spin and parity quantum numbers of the Higgs boson are presented, based on proton-proton collision data collected by the ATLAS experiment at the LHC. The Standard Model spin-parity $J^P = 0^+$ hypothesis is compared with alternative hypotheses using the Higgs boson decays $H \to \gamma\gamma, H \to ZZ^* \to 4$ leptons and $H \to WW^* \to l\nu l\nu$, as well as the combination of these channels. The analysed dataset corresponds to an integrated luminosity of 20.7 fb$^{-1}$ collected at a centre-of-mass energy of $\sqrt{s}$ = 8 TeV. For the $H \to ZZ^* \to 4$-lepton decay mode the dataset corresponding to an integrated luminosity of 4.6 fb$^{-1}$ collected at $\sqrt{s}$ = 7 TeV is added. The data are compatible with the Standard Model $J^P = 0^+$ quantum numbers for the Higgs boson, whereas all alternative hypotheses studied in this letter, namely some specific $J^P = 0^-, 1^+, 1^-, 2^+$ models, are excluded at confidence levels above 97.8%. This exclusion holds independently of the assumptions on the coupling strengths to the Standard Model particles and in the case of the $J^P = 2^+$ model, of the relative fractions of gluon-fusion and quark-antiquark production of the spin-2 particle. The data thus provide evidence for the spin-0 nature of the Higgs boson, with positive parity being strongly preferred.

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