A search for TeV-scale resonances decaying via a pair of Higgs bosons to the $b\bar{b}b\bar{b}$ final state is performed with 19.5 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=8$ TeV recorded by ATLAS in 2012. The search assumes a Standard Model Higgs boson with a mass of 125 GeV. The decay of each Higgs boson is reconstructed from a pair of $b$-tagged jets that have small angular separation and form a dijet system with transverse momentum greater than 200 GeV. The bulk Randall-Sundrum model with a warped extra dimension and a coupling of $k/\bar{M}_{\rm{Pl}} = 1.0$ is used as a benchmark to search for resonances, corresponding to the first Kaluza-Klein excitation mode of the graviton $G^{*}$, in the range between 500 GeV and 1500 GeV. No evidence of a signal is found, and upper limits on \sigma(pp\hspace{-1 mm}\to \hspace{-1 mm}G^{*}) \times {\rm BR}(G^{*}\hspace{-1 mm}\to\hspace{-1 mm}HH\hspace{-1mm}\to\hspace{-1mm}b\bar{b}b\bar{b}) are derived, giving an observed limit of 7 fb at the 95% confidence level for a KK graviton mass of 1 TeV. The benchmark model is excluded at the 95% confidence level for KK graviton masses between 590 GeV and 710 GeV.

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