Differential $t\bar{t}$ cross-section measurements using boosted top quarks in the all-hadronic final state with 139 fb$^{-1}$ of ATLAS data

Measurements are presented of single-, double-, and triple-differential cross-sections for boosted top-quark pair-production in 13 TeV LHC proton-proton collisions recorded by the ATLAS detector. The top quarks are observed through their hadronic decay and reconstructed as large-R jets with the leading jet having transverse momentum greater than 500 GeV. The largest background, the production of high-p$_{T}$ jets, is estimated using data-driven techniques. The observed data are unfolded to remove detector effects providing differential cross-section measurements at the particle-level. The particle-level cross-section times branching fraction, measured in a fiducial phase-space defined by requiring a leading and second-leading jet to have transverse momentum $p_{T}$ > 500 GeV and $p_{T}$ > 350 GeV, respectively, is $330 \pm 3 (stat.) \pm 38\ (syst.)$ fb. This is approximately 20% lower than Monte Carlo predictions with next-to-leading order (NLO) accuracy but consistent with within the theoretical uncertainties. Results are also presented at the parton-level, where the effects of top-quark decay, parton showering, and hadronization are also corrected such that the result can be compared to fixed-order next-to-next-to-leading order (NNLO) calculations. The parton-level cross-section, measured in a fiducial phase-space similar to that at particle-level and corrected for the top-quark branching fraction, is $1.94 \pm 0.02 (stat.) \pm 0.25 (syst.)$ pb. This is in agreement with the NNLO prediction within the measurement uncertainties. The differential cross-sections are compared with NLO and NNLO calculations. Reasonable agreement with the data is found for most NLO models while the NNLO predictions generally are in better agreement compared to the NLO predictions. The interpretation of the differential cross-sections using a Standard Model effective field-theory formalism is also performed.