In supersymmetric models, a large average stop mass $M_S$ is well known to both boost the lightest Higgs boson mass $m_h$ and also make radiative electroweak symmetry breaking unnaturally tuned. The case of “maximal mixing,” where the stop trilinear mixing term $A_t$ is set to give $A_t^2/M_S^2=6$, allows the stops to be as light as possible for a given $m_h$. Here we make the distinction between minimal $M_S$ and optimal naturalness, showing that the latter occurs for less-than-maximal mixing. Lagrange-constrained optimization reveals that the two coincide closely in the Minimal Supersymmetric Standard Model (MSSM)—optimally we have $5<A_t^2/M_S^2<6$. We discuss why the two are not generally expected to coincide beyond the MSSM, and explain that even within the MSSM, different models should not be compared based on the $M_S$ necessary to achieve a given $m_h$. The splitting between the two stop-mass eigenvalues $m_{{\tilde{t}}_2}-m_{{\tilde{t}}_1}$ is shown to be unconstrained by naturalness considerations.

• Received 12 November 2012

DOI:https://doi.org/10.1103/PhysRevD.86.115023