Double SM-like Higgs production at future e ⁺ e ⁻ colliders in the 3-Higgs Doublet Model under the S ₃ symmetry

In this paper, we present the production of double Standard Model (SM)-like Higgs [Formula: see text] at the future electron positron colliders within the framework of the [Formula: see text] model with three Higgs doublets (S3-3H) and no CP violation to describe beyond the SM Higgs Physics. We focus first on the numerically allowed parameter space of the model, taking into account theoretical bounds from perturbative unitarity and vacuum stability, as well as by data at the Large Hadron Collider (LHC) and the Tevatron. Double Higgs production in the S3-3H model can deviate from the SM predictions up to a few orders of magnitude in both the [Formula: see text] and the [Formula: see text] channels. Thus, our findings indicate that the S3-3H model can lead to sizable deviations from the SM predictions of Higgs production at future [Formula: see text] colliders. These results highlight the importance of studies at such colliders for searching for physics beyond the SM.