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.

On the vacuum stability of SUSY models

The existence of multiple non-equivalent minima of the scalar potential in SUSY models both raises technical challenges and introduces interesting physics. The technical challenges are now that one has to find several minima and evaluate which is the deepest, as well as calculate the tunneling time from a false vacuum to the true vacuum. We present here studies on the vacuum stability and color/charge breaking minima in the CMSSM and R parity violating minima in a B-L extended MSSM.

Stability of the CMSSM against sfermion VEVs

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.

Vevacious: A Tool For Finding The Global Minima Of One-Loop Effective Potentials With Many Scalars

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.

Stability of R parity in supersymmetric models extended by U(1)_{B-L}

We perform a study of the stability of R-parity-conserving vacua of a constrained version of the minimal supersymmetric model with a gauged U(1)_{B-L} which can conserve R-parity, using homotopy continuation to find all the extrema of the tree-level potential, for which we also calculated the one-loop corrections. While we find that a majority of the points in the parameter space preserve R-parity, we find that a significant portion of points which naively have phenomenologically acceptable vacua which conserve R-parity actually have deeper vacua which break R-parity through sneutrino VEVs. We investigate under what conditions the deeper R-parity-violating vacua appear. We find that while previous exploratory work was broadly correct in some of its qualitative conclusions, we disagree in detail.