Stabilization of the electroweak vacuum by a scalar threshold effect

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 treelevel 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.

Majorana dark matter through the Higgs portal under the vacuum stability lamppost

“…It is well known that the spontaneous breaking of a global U (1) symmetry have several disconnected and degenerate vacua (the phase of the vacuum expectation value 0|S|0 can be different in different regions of space, and actually we expect it to be different in casually disconnected regions), yielding dangerous domainwall structure in the early universe [43,44]. In the spirit of [43], it may be possible to explicitly break the symmetry introducing (possibly small) terms in V , such that the domain walls disappear before dominating the matter density of the universe, while leaving (pseudo-)Goldstone bosons and the same dark matter phenomenology [26]. 1 For simplicity, we restrict our considerations to the potential in (4), but generalizations are straightforward.…”

“…Note that the field values are the only functional arguments when talking about a potential like (4), and therefore the appropriate renormalization scale must also be at that scale. For λ 3 > 0, the third condition in (7) could potentially be violated only for field values φ around m h2 , regardless of the renormalization scale Q [26]. Consequently, the region of instability is found to be:…”

“…To obtain the matching conditions connecting the two theories, following [26] we integrate out the field S to obtain a Lagrangian of the form (56). Identifying the quadratic and quartic terms in the potential yields…”

“…The quartic interaction between the heavy scalar singlet and the Higgs doublet provides an essential contribution for the stabilization the scalar field potential [26]. When we refer to the stability of (4) at some energy Q (with the use of the couplings at that scale), we are assuming that the field values are at the scale Q.…”

“…Since the stability condition of the electroweak vacuum is strongly sensitive to new physics, from the phenomenological point of view it is clear that beyond SM physics models have to pass a sort of "stability test" [21][22][23]. Indeed, only new physics models that reinforce the requirement of a stable or metastable (but with τ > T U ) electroweak vacuum can be accepted as a viable UV completion of the SM [24][25][26][27][28][29][30][31][32][33][34][35].…”