Optimising Stop Naturalness

Abstract

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 optimisation 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 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.

14 pages, 3 figures. v2 and 3: extra content. v4: typos, PRD version

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• Supersymmetry, Naturalness, and Light Higgsinos
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• Supergravity gauge theories strike back: There is no crisis for SUSY but a new collider may be required for discovery
• Stop on Top: SUSY Parameter Regions, Fine-Tuning Constraints
• 1-loop SQCD corrections to the decay of top-squarks to charm and neutralino in the generic MSSM
• Tagging a mono-top signature in Natural SUSY
• Investigating the Quantum Properties of Jets and the Search for a Supersymmetric Top Quark Partner with the ATLAS Detector