Constraining the Natural MSSM through tunneling to color-breaking vacua at zero and non-zero temperature

We re-evaluate the constraints on the parameter space of the minimal supersymmetric standard model from tunneling to charge- and/or color-breaking minima, taking into account thermal corrections. We pay particular attention to the region known as the Natural MSSM, where the masses of the scalar partners of the top quarks are within an order of magnitude or so of the electroweak scale. These constraints arise from the interaction between these scalar tops and the Higgs fields, which allows the possibility of parameter points having deep charge- and color-breaking true vacua. In addition to requiring that our electro-weak-symmetry-breaking, yet QCD- and electromagnetism-preserving vacuum has a sufficiently long lifetime at zero temperature, also demanding stability against thermal tunneling further restricts the allowed parameter space.