Vacuum stability conditions from copositivity criteria
By K. Kannike. 2012
310 citations recorded by the source corpus.
A scalar potential of the form $\lambda_{ab} \varphi_{a}^{2} \varphi_{b}^{2}$ is bounded from below if its matrix of quartic couplings λab is copositive—positive on non-negative vectors. Scalar potentials of this form occur naturally for scalar dark matter stabilised by a ℤ2 symmetry. Copositivity criteria allow us to derive analytic necessary and sufficient vacuum stability conditions for the matrix λab. We review the basic properties of copositive matrices and analytic criteria for copositivity. To illustrate these, we re-derive the vacuum stability conditions for the inert doublet model in a simple way, and derive the vacuum stability conditions for the ℤ2 complex singlet dark matter, and for the model with both a complex singlet and an inert doublet invariant under a global U(1) symmetry.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/2c56a3ddfa8074be7dfb31b4a3b5a425360ad921
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Citations in the corpus
- Building and testing models with extended Higgs sectors (2017, background): “Since the potential is now expressed in terms of quadratic quantities φ†φ, S(2), A(2), the stability conditions can be derived exactly with the copositivity criteria [363].”
- Dark matter and neutrino masses from a scale-invariant multi-Higgs portal (2015, background): “It can be shown [72–76] that this is equivalent to the conditions”
- Vacuum stability of a general scalar potential of a few fields (2016, methodology): “Copositivity has found wide use in the field of convex optimisation, and was first used to derive vacuum stability conditions in [6].”