The ATLAS experiment at the LHC has determined the couplings of the Higgs boson to other particles, as well as its mass, using the combination of measurements from multiple production and decay channels with up to 4.8 fb$^{-1}$ of $pp$ collision data at $\sqrt{s}=7$~TeV and 20.3 fb$^{-1}$ at $\sqrt{s}=8$~TeV. In this study, the mass dependence of the couplings is probed and the coupling measurements are interpreted in different extensions of the Standard Model. An indirect search is performed for a composite Higgs boson, an additional electroweak singlet, an additional electroweak doublet (two-Higgs-doublet model), a simplified Minimal Supersymmetric Standard Model, and a Higgs portal to dark matter. The measured production and decay rates of the observed Higgs boson in the $h\to\gamma\gamma$, $h\to ZZ^*\to 4\ell$, $h\to WW^*\to \ell\nu\ell\nu$, $h\to\tau\tau$, and $h\to b\bar{b}$ channels, the measured mass in the $h\to\gamma\gamma$ and $h\to ZZ^*\to 4\ell$ decay modes, and the measured upper limit on the rate of the $Zh \to \ell\ell + E_{{\textrm T}}^{\textrm{miss}}$ process are used to constrain parameters of these models.

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