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.
Acceptance x efficiency versus $\kappa_{2V}$ for non-resonant signal of $HH$.
Acceptance x efficiency versus resonance mass for both narrow and broad resonance $X$ to $HH$.
Post-fit mass distribution of the $HH$ candidates in the signal region. The expected background is shown after the profile-likelihood fit to data with the background-only hypothesis; the narrow-width resonant signal at 800 GeV and the non-resonant signal at $\kappa_{2V}$ = 3 are overlaid, both normalised to the corresponding observed upper limits on the cross-section.
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