Large One-Loop Effects of BSM Triple Higgs Couplings on Double Higgs Production at $e^+e^-$ Colliders

The measurement of the Higgs boson self-coupling is crucial for our understanding of the nature of electroweak symmetry breaking and potential physics beyond the Standard Model (BSM). In this work, we study in the framework of the 2-Higgs-Doublet Model (2HDM) the impact of one-loop corrections to triple Higgs couplings (THCs) on the pair production of two Standard Model (SM)-like Higgs bosons $h$ at future high-energy $e^+ e^-$ colliders, focusing on the $e^+ e^- \to Zhh$ process. By including the one-loop corrections to the THCs relevant for this process, i.e. the coupling between three SM-like Higgs bosons, $\lambda_{hhh}$, and between the non-SM-like Higgs $H$, assumed to be heavier, and two SM-like Higgs bosons, $\lambda_{hhH}$, we account for the leading one-loop corrections to the di-Higgs production cross section. We show that the one-loop corrected THC $\lambda_{hhh}$ can be enhanced up to nearly six times its SM value, which substantially enhances the di-Higgs production cross section w.r.t. the tree-level prediction, even in the alignment limit. On the other hand, one-loop corrections to $\lambda_{hhH}$ can also enhance its value, potentially yielding to more prominent heavy Higgs $H$ resonant production. We explore the sensitivity to the loop-corrected $\lambda_{hhh}$ and the possible access to $\lambda_{hhH}$ via the $H$ resonant peak at a future high-energy $e^+e^-$ collider, such as the ILC. We highlight the fact that including the one-loop corrected THCs can enhance the sensitivity to the $H$ resonant peak, and therefore to $\lambda_{hhH}$. Finally, we discuss the required experimental precision at future $e^+e^-$ colliders necessary to achieve these sensitivities.