Confronting Higgs couplings from D-term extensions and natural SUSY at the LHC and ILC

Non-decoupling D-term extensions of the MSSM enhance the tree-level Higgs mass compared to the MSSM; therefore, they relax fine-tuning and may allow lighter stops with rather low masses even without maximal mixing. We present the anatomy of various non-decoupling D-term extensions of the MSSM and explore the potential of the LHC and of the International Linear Collider (ILC) to determine their deviations in the Higgs couplings with respect to the Standard Model. Depending on the mass of the heavier Higgs mH, such deviations may be constrained at the LHC and determined at the ILC. We evaluate the Higgs couplings in different models and study the prospects for a model distinction at the different stages of the ILC at root s = 250, 500 and 1000 GeV, including the full luminosity upgrade and compare it with the prospects at HL-LHC.