Scale genesis and gravitational wave in a classically scale invariant extension of the standard model

TL;DR

The paper tackles the origin of the electroweak scale within a classically scale-invariant framework by invoking a nonperturbative, gauge-invariant scalar-bilinear condensation in a hidden SU($N_c$) sector that generates a dynamical scale transmitted to the SM through a Higgs portal. Using a path-integral/Hubbard–Stratonovich approach, the authors derive a mean-field effective theory with auxiliary fields, compute the finite-temperature effective potential, and show the scale phase transition can be strongly first-order at a temperature $T_S$ above the EW transition temperature $T_{EW}$ yet below a few hundred GeV. They select a benchmark with DM and Higgs-portal couplings that yields a consistent DM relic abundance and a strong scale transition around $T_S\sim 0.32$ TeV, which sources a stochastic GW background. The GW analysis, employing established formulas for bubble collisions, MHD turbulence, and especially sound waves, indicates the signal is dominated by sound waves with a peak near $\nu\sim 0.1$–1 Hz and $\Omega_{\rm GW} \hat h^2 \sim 10^{-14}$–$10^{-13}$, potentially observable by DECIGO. This work thus links EW-scale genesis, hidden-sector dynamics, and DM phenomenology to a testable GW signal in the near future.

Abstract

We assume that the origin of the electroweak (EW) scale is a gauge-invariant scalar-bilinear condensation in a strongly interacting non-abelian gauge sector, which is connected to the standard model via a Higgs portal coupling. The dynamical scale genesis appears as a phase transition at finite temperature, and it can produce a gravitational wave (GW) background in the early Universe. We find that the critical temperature of the scale phase transition lies above that of the EW phase transition and below few $O(100)$ GeV and it is strongly first-order. We calculate the spectrum of the GW background and find the scale phase transition is strong enough that the GW background can be observed by DECIGO.

Figures (5)

• Figure 1: The spin-independent elastic cross section $\sigma_{SI}$ of DM off the nucleon as a function of $m_{\rm DM}$ for $N_f=2,N_c=6$. The black solid line stands for the central value of the LUX upper bound Akerib:2016vxi with one (green) and two (yellow) $\sigma$ bands, and the black dotted line indicates the sensitivity of XENON1T Aprile:2012zxAprile:2015uzo.
• Figure 2: The effective interaction $\phi^2h^2$ generated by the $S$ loop effect.
• Figure 3: The EW phase transition. The transition occurs around $T=T_\text{EW}\simeq 0.161$ TeV.
• Figure 4: Left: The scale phase transition. The strong first-order transition occurs at $T=T_{S}=0.323$ TeV. Right: The effective potential $V_{\rm eff}(f,0,T)/\Lambda_H^4$ against $f^{1/2}$ at the critical temperature $T=T_{S}=0.323$ TeV. The potential energy density at the origin is subtracted from $V_{\rm eff}$.
• Figure 5: The GW background spectrum. The doted lines are the four different sensitivities of eLISA, where the labels ("C1", $\cdots$,"C4") correspond to the configurations listed in Table 1 in Caprini:2015zlo. The data sets of their configurations are taken from eLISAdata. The dashed lines are sensitivities of three different designs ("Pre-DECIGO", "FP-DECIGO" and "Correlation") of DECIGO Seto:2001qf. The parameter $\gamma$ is defined in \ref{['chi']}.