A search for Higgs boson pair production via vector-boson fusion (VBF) in the $b\bar{b}b\bar{b}$ final state is carried out with the ATLAS experiment using 126 fb$^{-1}$ of proton-proton collision data delivered at $\sqrt{s} = 13$ TeV by the Large Hadron Collider. This search is sensitive to VBF production of additional heavy bosons that may decay into Higgs boson pairs, and in a non-resonant topology it can constrain the quartic coupling between the Higgs bosons and vector bosons. No significant excess relative to the Standard Model expectation is observed, and limits on the production cross-section are set at the 95 % confidence level for a heavy scalar resonance in the context of an extended Higgs sector, and for non-resonant Higgs boson pair production. Interpretation in terms of the coupling between a Higgs boson pair and two vector bosons is also provided: coupling values normalised to the Standard Model expectation of $\kappa_{2V} < -0.43$ and $\kappa_{2V} > 2.56$ are excluded at the 95 % confidence level in data.
A search for resonant and non-resonant pair production of Higgs bosons in the $b\bar{b}\tau^+\tau^-$ final state is presented. The search uses 36.1 fb$^{-1}$ of $pp$ collision data with $\sqrt{s}= 13$ TeV recorded by the ATLAS experiment at the LHC in 2015 and 2016. The semileptonic and fully hadronic decays of the $\tau$-lepton pair are considered. No significant excess above the expected background is observed in the data. The cross-section times branching ratio for non-resonant Higgs boson pair production is constrained to be less than 30.9 fb, 12.7 times the Standard Model expectation, at 95% confidence level. The data are also analyzed to probe resonant Higgs boson pair production, constraining a model with an extended Higgs sector based on two doublets and a Randall-Sundrum bulk graviton model. Upper limits are placed on the resonant Higgs boson pair production cross-section times branching ratio, excluding resonances $X$ in the mass range $305~{\rm GeV} < m_X < 402~{\rm GeV}$ in the simplified hMSSM minimal supersymmetric model for $\tan\beta=2$ and excluding bulk Randall-Sundrum gravitons $G_{\mathrm{KK}}$ in the mass range $325~{\rm GeV} < m_{G_{\mathrm{KK}}} < 885~{\rm GeV}$ for $k/\overline{M}_{\mathrm{Pl}} = 1$.
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