Exploring Higgs EFT in $t\bar{t}hh$ at High Luminosity LHC

The non-resonant production of a Higgs boson pair in association with a top-antitop quark pair ($pp\rightarrow t\bar{t}hh$) has only recently begun to be explored at the Large Hadron Collider (LHC) and provides a unique and largely uncharted probe of the top-Higgs sector, offering complementary sensitivity to the Higgs self-coupling and higher-dimensional interactions beyond the Standard Model. In this work, we present a detailed study of this process within the framework of Higgs Effective Field Theory (HEFT) at the High-Luminosity LHC (HL-LHC). A comparative analysis is performed using a traditional cut-based approach in the single-lepton channel and a multivariate parametric boosted decision tree method in both single-lepton and dilepton final states. We derive one- and two-parameter limits at 95\% confidence level on the HEFT couplings $\delta\kappa_\lambda$, $c_2$, $c_{2g}$, and $c_{tg}$. The projected bound on $\delta\kappa_\lambda$ is weaker than current experimental constraints from dedicated Higgs-pair measurement; however, this coupling plays a critical role in shaping the multidimensional allowed parameter space. For the remaining HEFT couplings, where no direct experimental limits currently exist, our results provide the first sensitivity projections in the $t\bar{t}hh$ channel. Overall, this study demonstrates the strong potential of the $t\bar{t}hh$ production process to probe extended Higgs and top-quark interactions beyond the Standard Model through the exploitation of the $t\bar{t}hh$ data at the HL-LHC.