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Searches are performed for nonresonant and resonant di-Higgs boson productionin the $b\bar{b}\gamma\gamma$ final state. The data set used corresponds to anintegrated luminosity of 139 fb$^{-1}$ of proton-proton collisions at acenter-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERNLarge Hadron Collider. No excess above the expected background is found andupper limits on the di-Higgs boson production cross sections are set. A 95%confidence-level upper limit of 4.2 times the cross section predicted by theStandard Model is set on $pp \rightarrow HH$ nonresonant production, where theexpected limit is 5.7 times the Standard Model predicted value. The expectedconstraints are obtained for a background hypothesis excluding $pp \rightarrowHH$ production. The observed (expected) constraints on the Higgs bosontrilinear coupling modifier $\kappa_{\lambda}$ are determined to be $[-1.5,6.7]$ $([-2.4, 7.7])$ at 95% confidence level, where the expected constraintson $\kappa_{\lambda}$ are obtained excluding $pp \rightarrow HH$ productionfrom the background hypothesis. For resonant production of a new hypotheticalscalar particle $X$ ($X \rightarrow HH \rightarrow b\bar{b}\gamma\gamma$),limits on the cross section for $pp \to X \to HH$ are presented in thenarrow-width approximation as a function of $m_{X}$ in the range $251 \leqm_{X} \leq 1000$ GeV. The observed (expected) limits on the cross section for$pp \to X \to HH$ range from 640 fb to 44 fb (391 fb to 46 fb) over theconsidered mass range.

physical review. d/physical review. d.

Search for Higgs boson pair production in the two bottom quarks plus two  photons final state in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS  detector