The price of being SM-like in SUSY

We compute the tuning in supersymmetric models associated with the constraints from collider measurements of the Higgs couplings to fermions and gauge bosons. In supersymmetric models, a CP-even state with SM Higgs couplings mixes with additional, heavier CP-even states, causing deviations in the Higgs couplings from SM values. These deviations are reduced as the heavy states are decoupled with large soft masses, thereby exacerbating the tuning associated with the electroweak scale. This new source of tuning is different from that derived from collider limits on stops, gluinos and Higgsinos. It can be offset with large tan beta in the MSSM, however this compensating effect is limited in the NMSSM with a large Higgs-singlet coupling due to restrictions on large tan beta from electroweak precision tests. We derive a lower bound on this tuning and show that the level of precision of Higgs coupling measurements at the LHC will probe naturalness in the NMSSM at the few-percent level. This is comparable to the tuning derived from superpartner limits in models with a low messenger scale and split families. Instead the significant improvement in sensitivity of Higgs coupling measurements at the ILC will allow naturalness in these models to be constrained at the per-mille level, beyond any tuning derived from direct superpartner limits.