Strongly First-Order Electroweak Phase Transition and Classical Scale Invariance

Abstract

In this work, we examine the possibility of realizing a strongly first-order electroweak phase transition within the minimal classically scale invariant extension of the standard model (SM), previously proposed and analyzed as a potential solution to the hierarchy problem. By introducing one complex singlet scalar and three right-handed Majorana neutrinos, the scenario was successfully capable of achieving a radiative breaking of the electroweak symmetry (Coleman-Weinberg Mechanism), inducing non-zero masses for the SM neutrinos (seesaw mechanism), presenting a pseudoscalar dark matter candidate, and predicting the existence of a second $CP$-even boson in addition to the 125 GeV scalar. We construct the full finite-temperature one-loop effective potential of the model, including the resummed thermal daisy loops, and demonstrate that finite-temperature effects induce a first-order electroweak phase transition. Requiring the thermally-driven first-order phase transition to be sufficiently strong further constrains the model's parameter space; in particular, an $\mathcal{O}(0.01)$ fraction of the dark matter in the universe may be simultaneously accommodated with a strongly first-order electroweak phase transition. Moreover, such a phase transition disfavors right-handed Majorana neutrino masses above several hundreds of GeV, confines the pseudoscalar dark matter masses to $\sim 1$-2 TeV, predicts the mass of the second $CP$-even scalar to be $\sim 100$-300 GeV, and requires the mixing angle between the $CP$-even components of the SM doublet and the complex singlet to lie within the range $0.2\lesssim \sin \omega \lesssim 0.4$. The obtained results are displayed in comprehensive exclusion plots, identifying the viable regions of the parameter space. Many of these predictions lie within the reach of the next LHC run.

18 pages, 9 figures. Published version, typos corrected, references added

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