Abstract
Classical scale invariance (CSI) may shed light on the weak scale origin, but the realistic CSI extension to the standard model requires a bosonic trigger. We propose a scalar dark matter (DM) field $X$ as the trigger, establishing a strong connection between the successful radiative breaking of CSI and DM phenomenologies. The latter forces the breaking scale to approximately $\mathcal{O}(\mathrm{TeV})$. It brightens the test prospect of this scenario via a gravitational wave, a sharp prediction of CSI phase transition (CSIPT), which is first order and has strong supercooling. Moreover, we carefully deal with some techniques which are commonly used to analyze CSIPT but may be missed. In particular, we clarify the imprecision of Witten's formula used in the single field case to calculate the bubble nucleation rate and stress that the essence of Witten's approximation is the validity of high-temperature expansion.
Highlights
The origin and stabilization of the weak scale are the fundamental questions of the particle standard model (SM), and they lead the progresses of modern particle physics
Confronting the correct dark matter (DM) relic density and suppressed DM-nucleon recoil rate, we focus on two frequently studied cases: (i) In Gildener-Weinberg approach on the valley, the tree-level potential admits a valley at some scale μGW, and one can apply the Gildener-Weinberg approach [16] to study CSI spontaneously breaking (CSISB)
(ii) In the Coleman-Weinberg approach in the decoupling limit, if the Higgs interactions with the scalon and trigger are irrelevantly small, CSISB by the scalon is reduced to the conventional single field case, and one can apply the Coleman-Weinberg (CW) approach [17], whereas the electroweak symmetry breaking (EWSB) proceeds via the usual mechanism
Summary
The origin and stabilization of the weak scale are the fundamental questions of the particle standard model (SM), and they lead the progresses of modern particle physics. (ii) In the Coleman-Weinberg approach in the decoupling limit, if the Higgs interactions with the scalon and trigger are irrelevantly small, CSISB by the scalon is reduced to the conventional single field case, and one can apply the Coleman-Weinberg (CW) approach [17], whereas the EWSB proceeds via the usual mechanism. Both scenarios leave viable parameter spaces, with scalon VEV at the multi-TeV scale and a heavy DM at the TeV scale.
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