Radiatively generated maximal mixing scenario for the Higgs boson mass and the least fine-tuned minimal supersymmetric standard model

We argue that given the experimental constraints on the Higgs boson mass the least fine-tuned parameter space of the minimal supersymmetric standard model is with negative top-squark masses squared at the grand unification scale. While the top-squark mass squared is typically driven to positive values at the weak scale, the contribution to the Higgs boson mass squared parameter from the running can be arbitrarily small, which reduces the fine-tuning of electroweak symmetry breaking. At the same time the top-squark mixing is necessarily enhanced and the maximal mixing scenario for the Higgs boson mass can be generated radiatively even when starting with negligible mixing at the unification scale. This highly alleviates constraints on possible models for supersymmetry breaking in which fine-tuning is absent.