We investigate high scale boundary conditions on the quartic Higgs couplings and their β functions in the type-II two Higgs doublet model and the inert doublet model. These conditions are associated with two possible UV physics scenarios: the multiple point principle, in which the potential exhibits a second minimum at M Pl , and asymptotic safety, where the scalar couplings run toward an interacting UV fixed point at high scales. We employ a renormalization group running at two loops and apply theoretical and experimental constraints to their parameter spaces. We find neither model can simultaneously accommodate the multiple point principle while also providing realistic masses for both the Higgs and the top quark. However, we do find regions of parameter space compatible with asymptotic safety.

We investigate Planck-scale boundary conditions on Higgs quartic interactions and their β functions in the Standard Model augmented by an additional complex scalar. We use renormalization group running at two loops, and include both theoretical and experimental constraints. We find that the boundary condition λ ¼ β λ ¼ 0 at the Planck scale is compatible with the current Higgs and top mass measurements, but requires additional scalars lighter than about 600 GeV.

The Higgs boson quartic self-coupling in the Standard Model appears to become zero just below the Planck scale, with interesting implications to the stability fo the Higgs vacuum at high energies. We review the Multiple Point Principle that suggests the quartic self-coupling should vanish exactly at the Planck scale. Although this vanishing is not consistent with the Standard Model, we investigate Higgs sectors extended with additional states to test whether one may satisfy the high scale boundary condition while maintaining the observed Higgs mass. We also test these scenarios to ensure the stability of the vacuum at all energies below the the Planck scale and confront them with experimental results from the LHC and Dark Matter experiments.