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.
The recent discovery of a Higgs boson by the LHC experiments has profound implications for supersymmetric models. In particular, in the context of restricted models, such as the supergravity-inspired constrained minimal supersymmetric standard model,
one finds that preferred regions in parameter space have large soft supersymmetry-breaking trilinear couplings. This potentially gives rise to charge- and/or color-breaking minima besides those with the correct breaking of $SU(2)_L times U(1)_Y$. We investigate the stability of parameter points in this model against tunneling to possible deeper color- and/or charge-breaking minima of the one-loop effective potential. We find that allowed regions of the parameter space with light staus or with light stops are seriously constrained by the requirement that the tunneling time out of the normal electroweak-symmetry-breaking vacuum is more than a fifth of the age of the known Universe. We also find that thumb rule conditions on Lagrangian parameters based on specific directions in the tree-level potential are of limited use.
Several extensions of the Standard Model of particle physics contain additional scalars implying a more complex scalar potential compared to that of the Standard Model. In general these potentials allow for charge and/or color breaking minima besides
the desired one with correctly broken SU(2)_L times U(1)_Y . Even if one assumes that a metastable local minimum is realized, one has to ensure that its lifetime exceeds that of our universe. We introduce a new program called Vevacious which takes a generic expression for a one-loop effective potential energy function and finds all the tree-level extrema, which are then used as the starting points for gradient-based minimization of the one-loop effective potential. The tunneling time from a given input vacuum to the deepest minimum, if different from the input vacuum, can be calculated. The parameter points are given as files in the SLHA format (though is not restricted to supersymmetric models), and new model files can be easily generated automatically by the Mathematica package SARAH. This code uses HOM4PS2 to find all the minima of the tree-level potential, PyMinuit to follow gradients to the minima of the one-loop potential, and CosmoTransitions to calculate tunneling times.
Results are presented for the two-body decays of mesons into light neutralinos and from the first complete calculation of the loop-induced decays of kaons to pions plus light neutralinos and of B mesons to kaons plus light neutralinos. The branching
ratios are shown to be strongly suppressed within the MSSM with minimal flavor violation, and no bounds on the neutralino mass can be inferred from experimental data, i.e. a massless neutralino is allowed.
Lepton-flavour violating tau-decays are predicted in many extensions of the Standard Model at a rate observable at future collider experiments. In this article we focus on the decay tau to mu mu antimu, which is a promising channel to observe lepton-
flavour violation at the Large Hadron Collider LHC. We present analytic expressions for the differential decay width derived from a model-independent effective Lagrangian with general four-fermion operators, and estimate the experimental acceptance for detecting the decay tau to mu mu antimu at the LHC. Specific emphasis is given to decay angular distributions and how they can be used to discriminate new physics models. We provide specific predictions for various extensions of the Standard Model, including supersymmetric, little Higgs and technicolour models.
