Abstract

Supersymmetric theories solve the hierarchy problem chiefly by virtue of a partner for the top quark, the stop, which contributes to the Higgs mass correction an equal amount with the opposite sign. The necessary soft breaking of supersymmetry makes the cancellation incomplete, with unnaturalness returning as the stop is decoupled. This leads us to consider stops as light as possible, subject to the extra constraint of the now observed Higgs mass of ~126 GeV. However we will show how ‘maximal mixing’ of the stops, while minimising their masses, contributes a new source of fine-tuning that is in fact dominant. Lagrange constrained maximisation of analytic expressions for the Higgs-stop interactions explicitly shows the optimal scenario to be near-maximal mixing. We explain why the splitting between the two stop mass eigenstates is entirely unconstrained. We introduce the NMSSM and explain its potential utility and limitations for boosting the Higgs mass naturally.