1205.3781 (Kristjan Kannike)

Vacuum Stability Conditions From Copositivity Criteria    [PDF]

Kristjan Kannike

A scalar potential of the form \lambda_ab \phi_a^2 \phi_b^2 is bounded from below if its matrix of quartic couplings \lambda_ab is copositive -- positive on non-negative vectors. Scalar potentials of this form occur naturally for scalar dark matter stabilised by a Z_2 symmetry. Copositivity criteria allow to derive analytic necessary and sufficient vacuum stability conditions for the matrix \lambda_ab. 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 Z_2 complex singlet dark matter, and for the model with both a complex singlet and an inert doublet invariant under a global U(1) symmetry.

View original: http://arxiv.org/abs/1205.3781