Higgs couplings and naturalness in λ-SUSY

We study Higgs boson couplings in the large-lambda version of the Next-to-Minimal Supersymmetric Standard Model, known as lambda-SUSY. We find that the predicted deviations from the Standard Model (SM) in these couplings are inversely correlated with the amount of fine-tuning needed to accommodate a 126 GeV Higgs. In the most natural regions of parameter space, the 126 GeV Higgs has large admixtures of both the SM-singlet and the non-SM Higgs doublet scalars, and such regions are already ruled out by the LHC. Future improvements in the Higgs coupling measurements will either discover deviations from the SM, or put further stress on naturalness in lambda-SUSY. We present projections for future experiments and find that HL-LHC and the proposed e(+)e(-) Higgs factories can explore regions of parameter space that are fine-tuned at the level of up to 0.1%.