Search for non-resonant Higgs boson pair production in final states with leptons, taus, and photons in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search is presented for non-resonant Higgs boson pair production, targeting the $bbZZ$, 4$V$ ($V$ = $W$ or $Z$), $VV\tau \tau$, 4$\tau$, $\gamma \gamma VV$ and $\gamma \gamma \tau \tau$ decay channels. Events are categorised based on the multiplicity of light charged leptons (electrons or muons), hadronically decaying tau leptons, and photons. The search is based on a data sample of proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb${}^{-1}$. No evidence of the signal is found and the observed (expected) upper limit on the cross-section for non-resonant Higgs boson pair production is determined to be 17 (11) times the Standard Model predicted cross-section at 95% confidence level under the background-only hypothesis. The observed (expected) constraints on the $HHH$ coupling modifier, ${\kappa }_{\lambda }$, are determined to be $-6.2<{\kappa }_{\lambda }<11.6$ ($-4.5<{\kappa }_{\lambda }<9.6$) at 95% confidence level, assuming the Standard Model for the expected limits and that new physics would only affect ${\kappa }_{\lambda }$.