Gravitational Waves from Hidden QCD Phase Transition

TL;DR

This work analyzes gravitational waves produced by a first-order chiral phase transition in a hidden QCD-like sector, embedded in a scale-invariant SM extension and coupled to the SM via a real singlet S. Using the NJL model in a mean-field approximation, it computes the finite-temperature effective potential in a two-dimensional $(S,\sigma)$ field space, solves a multi-field bounce via a path-deformation method, and extracts tunneling parameters $T_t$, $\alpha$, and $\tilde{\beta}$ for four benchmark points. The resulting GW spectrum, including scalar-field, sound-wave, and turbulence contributions, is found to be dominated by sound waves with peak frequencies in the $0.01$–$1$ Hz range, making DECIGO potentially capable of detecting the signal (while LISA may be less sensitive). The study highlights the possibility of probing hidden strong dynamics and Higgs-portal couplings through future GW observations, while noting systematic NJL-model uncertainties and the need for lattice validation.

Abstract

Drastic changes in the early universe such as first-order phase transition can produce a stochastic gravitational wave (GW) background. We investigate the testability of a scale invariant extension of the standard model (SM) using the GW background produced by the chiral phase transition in a strongly interacting QCD-like hidden sector, which, via a SM singlet real scalar mediator, triggers the electroweak phase transition. Using the Nambu--Jona-Lasinio method in a mean field approximation we estimate the GW signal and find that it can be tested by future space based detectors.

Figures (8)

• Figure 1: The masses $(m_{\mathrm{DM}}, m_S)$ (left) and the hidden QCD scale $\Lambda_{\mathrm{H}}$ (right) versus $y$ for $\lambda_{H}=0.13$, $\lambda_{S}=0.08$ with two different values of $\lambda_{HS}$; $\lambda_{HS}=0.001$ (solid lines) and $0.002$ (dashed lines).
• Figure 2: The hidden QCD scale $\Lambda_{\mathrm{H}}$ against the DM mass $m_{\mathrm{DM}}$. In the colored region, $\left<h\right>=246~\mathrm{GeV}$, $m_h=125.09\pm 0.24~\mathrm{GeV}$, $\xi_{1}^{(1)}>0.99$ ($h$-$S$ mixing), $m_S\simeq 2m_{\mathrm{DM}}$, and the perturbativity and stability constraint (\ref{['scalars']}) are satisfied. We assumed the case for $\lambda_{HS},y \gtrsim 10^{-4}$. The color strength indicates the value of $y\left<S\right>/\Lambda_{\mathrm{H}}$ which is a measure of how the chiral symmetry is explicitly broken. The colored points are the benchmark points; Cases A (red), B (green), C (purple), and D (blue) are defined in Table \ref{['CaseABCD']}.
• Figure 3: The temperature dependence of $\left<\sigma\right>/T$ (dark colored) and $\left<S\right>/T$ (light colored) for each benchmark point. Cases A (top left), B (top right), C (bottom left), and D (bottom right) are defined in Table \ref{['CaseABCD']}.
• Figure 4: The $\sigma$ field dependence of the field renormalization constant $Z_{\sigma}(S=0,\sigma,T)$ for $T/\Lambda_{\mathrm{H}}=0~\mathrm{(black)},~0.01~\mathrm{(red)},~0.02~\mathrm{(blue)},~\mathrm{and}~0.03~\mathrm{(purple)}$.
• Figure 5: Top: The contour plot of the effective potential $V_{\mathrm{EFF}}$ in (\ref{['VEFF']}) with $T/\Lambda_{\mathrm{H}}=0.0570$ for Case A, defined in Table \ref{['CaseABCD']}. The black dashed line stands for the initial path $S_0(\sigma)$ and the black solid line is the path $S_{15}(\sigma)$ with $|k\hat{N}_{15}(\sigma)|/ S_{15}(\sigma) < 10^{-2}$. Bottom: The region enclosed by the box near the false vacuum in the top figure is zoomed.