Higgs Couplings and Naturalness in $\lambda$-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.