Sensitivity to triple Higgs couplings via di-Higgs production in the 2HDM at $$e^+e^-$$ colliders

An important task at future colliders is the investigation of Higgs-boson sector. Here measurement triple Higgs coupling(s) plays a special role. Based on previous analyses, within framework Two Doublet Models (2HDM) type~I and~II, we define and analyze several two-dimensional benchmark planes, that are over large parts in agreement with all theoretical experimental constraints. For these planes evaluate di-Higgs production cross sections high-energy $e^+e^-$ colliders, such as ILC or CLIC. We consider two different channels for neutral pairs $h_i h_j=hh,hH,HH,AA$: $e^+e^- \to h_i h_j Z$ \nu \bar \nu$. In both various couplings contribute substantially. find regions strong enhancement channel SM-like light bosons and/or very involving one heavy 2HDM bosons, offering interesting prospects The mechanisms leading to enhanced analyzed detail. propose use section distributions invariant mass final where contributions from intermediate resonant non-resonant BSM play crucial outline which process center-of-mass energy would be best suited probe corresponding couplings.