Abstract
Classically scale-invariant models are attractive not only because they may offer a solution to the long-standing gauge hierarchy problem, but also due to their role in facilitating strongly supercooled cosmic phase transitions. In this paper, we investigate the interplay between these two aspects. We do so in the context of the electroweak phase transition (EWPT) in the minimal scale-invariant theory. We find that the amount of supercooling generally decreases for increasing scalar couplings. However, the stabilization of the electroweak scale against the Planck scale requires the absence of Landau poles in the respective energy range. Scalar couplings at the TeV scale can therefore not become larger than \U0001d4aa(10−1). As a consequence, all fully consistent parameter points predict the EWPT not to complete before the QCD transition, which then eventually triggers the generation of the electroweak scale. We also discuss the potential of the model to give rise to an observable gravitational wave signature, as well as the possibility to accommodate a dark matter candidate.
Highlights
JHEP12(2019)158 needs to be communicated to the Standard Model (SM) sector, which is usually realized via the portal term between the SM Higgs doublet and the new scalar(s), see e.g. ref. [3]
Note that we studied both possibilities of identifying the SM-like Higgs particle with one of the eigenstates of the mass matrix from eq (2.4), i.e. either with the heavier or lighter one
As was already demonstrated in ref. [27], the value of the portal coupling λsr at the scale of radiative symmetry breaking is crucial for the successful implementation of the minimal scale-invariant model
Summary
The minimal classically scale-invariant extension of the Standard Model (SM) which is consistent with current phenomenological observations and which can avoid Landau poles below the Planck scale, features two real scalar gauge singlets [27]. Based on the described symmetry breaking pattern, one can identify the terms in the potential (2.1) from which the masses of the scalar particles arise. The field-dependent tree-level masses for r and the Goldstone bosons read m2r(φc, sc). While the temperature-dependent terms will be introduced, here we define the usual Coleman-Weinberg potential [16] employing the MS renormalization scheme and Landau gauge. The number of real degrees of freedom of particle species i (including an additional minus sign for fermionic fields) is denoted as ni. The sum in eq (2.7) is taken over all relevant fields, i ∈ {+, −, r, χ, t, W, Z}, thereby consistently including the leading fermionic (top quark) and gauge boson (W and Z) SM contributions associated with the following field-dependent tree-level masses m2t (φc) yt.
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