Projected sensitivity of Higgs boson pair production combining the $b\bar{b}\gamma\gamma$ and $b\bar{b}\tau^{+}\tau^{-}$ final states with the ATLAS detector at the HL-LHC

A combination of projection studies of non-resonant Higgs boson pair production in the $b\bar{b}\tau^+\tau^-$ and $b\bar{b}\gamma\gamma$ final states with the ATLAS detector is presented, assuming 3000 $\text{fb}^{-1}$ of $pp$ collisions and a centre-of-mass energy of $\sqrt{s}=14$ TeV at the HL-LHC. The projected results are based on extrapolations of the Run 2 analyses conducted with 139 $\text{fb}^{-1}$ of data at $\sqrt{s}=13$ TeV, with revised assumptions on the systematic uncertainties. The estimated significance for the observation of the Standard Model Higgs boson pair production with (without) systematic uncertainties is $3.2 \,\sigma$ ($4.6 \,\sigma$), and the signal strength relative to the Standard Model prediction is expected to be measured with an accuracy of $_{-31}^{+34}$% ($\pm23$%). The modifier of the trilinear Higgs boson self-coupling, $\kappa_\lambda$, is projected to be constrained to the $1\sigma$ interval $[0.5, 1.6]$ ($[0.6, 1.5]$) with (without) systematic uncertainties, assuming that other Higgs boson couplings are consistent with the Standard Model.