Charge and color breaking constraints in the Minimal Supersymmetric Standard Model associated with the bottom Yukawa coupling

Testing the stability of the electroweak vacuum in any extension of the Standard Model Higgs sector is of great importance to verify the consistency of the theory. Multi-scalar extensions as the Minimal Supersymmetric Standard Model generically lead to unstable configurations in certain regions of parameter space. An exact minimization of the scalar potential is rather an impossible analytic task. To give handy analytic constraints, a specific direction in field space has to be considered which is a simplification that tends to miss excluded regions, however good to quickly check parameter points. We describe a yet undescribed class of charge and color breaking minima as they appear in the Minimal Supersymmetric Standard Model, exemplarily for the case of non-vanishing bottom squark vacuum expectation values constraining the combination μYbμYb in a non-trivial way. Contrary to famous A-parameter bounds, we relate the bottom Yukawa coupling with the supersymmetry breaking masses. Another bound can be found relating soft breaking masses and μ only. The exclusions follow from the tree-level minimization and can change dramatically using the one-loop potential. Estimates of the lifetime of unstable configurations show that they are either extremely short- or long-lived.