Abstract
Abstract We show how a heavy scalar singlet with a large vacuum expectation value can evade the potential instability of the Standard Model electroweak vacuum. The quartic interaction between the heavy scalar singlet and the Higgs doublet leads to a positive tree-level threshold correction for the Higgs quartic coupling, which is very effective in stabilizing the potential. We provide examples, such as the see-saw, invisible axion and unitarized Higgs inflation, where the proposed mechanism is automatically implemented in well-defined ranges of Higgs masses.
Highlights
Stabilizing the Higgs with a scalar singletTo explore the impact of an additional singlet scalar on the stability of the Higgs potential, we consider a tree-level scalar potential of the form
The effect occurs at tree level and can be sizable and, in general, dominant over loop contributions
We show how a heavy scalar singlet with a large vacuum expectation value can evade the potential instability of the Standard Model electroweak vacuum
Summary
To explore the impact of an additional singlet scalar on the stability of the Higgs potential, we consider a tree-level scalar potential of the form. H is the Higgs doublet, S is a complex scalar field, and V0 is the most general renormalizable potential that respects a global abelian symmetry under which only S is charged. We will consider here a single complex scalar, most of our conclusions remain valid in the case of multi-Higgs doublets or real singlet fields (with a Z2 parity replacing the abelian symmetry). A nonzero vev of S, which is crucial for our mechanism to work, spontaneously breaks the global symmetry (or the Z2 parity, for a real singlet) giving rise to a potentially dangerous Goldstone boson (or domain walls). The presence of the new scalar field S modifies the analysis of the stability conditions of the Higgs potential. The relevant renormalization group equations (RGEs) above the scale MS = 2λSw are, at one-loop:. If the singlet mass MS is below the SM instability scale ΛI and (λHS/4π) ln(ΛI /MS) is large enough, the positive contribution to the RGE equation for λH can prevent it from becoming negative
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