Dark Confinement and Chiral Phase Transitions: Gravitational Waves vs Matter Representations

TL;DR

The study investigates gravitational-wave signals from dark gauge-fermion sectors undergoing confinement and chiral phase transitions using the PNJL framework, comparing SU(3) theories with fundamental, adjoint, and two-index symmetric fermions. It calculates bubble nucleation, GW parameters, and spectra, finding that the two-index symmetric representation yields the strongest first-order transition and the best BBO prospects, while all models exhibit large inverse durations tilde{beta} ~ O(10^4). The work demonstrates how representation and model details shape detectability, with BBO potentially probing Tc in the tens-to-hundreds GeV range for certain cases, and provides a versatile methodology applicable to composite dynamics beyond the Standard Model. It also offers insights into how thin-wall dynamics and cubic terms in the condensate energy influence the phase-transition strength and GW output, informing future model-building in dark sectors and their experimental tests.

Abstract

We study the gravitational-wave signal stemming from strongly coupled models featuring both, dark chiral and confinement phase transitions. We therefore identify strongly coupled theories that can feature a first-order phase transition. Employing the Polyakov-Nambu-Jona-Lasinio model, we focus our attention on SU(3) Yang-Mills theories featuring fermions in fundamental, adjoint, and two-index symmetric representations. We discover that for the gravitational-wave signals analysis, there are significant differences between the various representations. Interestingly we also observe that the two-index symmetric representation leads to the strongest first-order phase transition and therefore to a higher chance of being detected by the Big Bang Observer experiment. Our study of the confinement and chiral phase transitions is further applicable to extensions of the Standard Model featuring composite dynamics.

Figures (12)

• Figure 1: Fundamental representation: expectation value of the Polyakov loop $\langle\ell\rangle$ and the chiral condensate $\sigma$ as a function of temperature. The latter is normalised to its value at vanishing temperature $\sigma_0$. We present the polynomial and logarithmic fitting of the Polyakov-loop potential.
• Figure 2: Adjoint representation: expectation value of the Polyakov loop $\langle\ell\rangle$ and the constituent quark mass $M$ as a function of temperature. The latter is normalised to its value at vanishing temperature $M_0$. We present the polynomial and logarithmic fitting of the Polyakov-loop potential.
• Figure 3: Two-index symmetric representation: expectation value of the Polyakov loop $\langle\ell\rangle$ and the constituent quark mass $M$ as a function of temperature. The latter is normalised to its value at vanishing temperature $M_0$. We present the polynomial and logarithmic fitting of the Polyakov-loop potential.
• Figure 4: Wave-function renormalization $Z_\sigma^{-1}$ for different temperatures as a function of the chiral condensate $\sigma$ normalised to its value at zero temperature $\sigma_0$.
• Figure 5: Fundamental representation: The GW parameters $\tilde{\beta}$ (top left) and $\alpha$ (top right) as well as the observables $M$, $f_{\pi}$, and $m_\sigma$ (bottom) as a function of the couplings $G_S = k_{G_S}\cdot 4.6\,\text{GeV}^{-2}$ and $G_D = k_{G_D}\cdot(-743\,\text{GeV}^{-5})$. We use $T_c=100$ GeV, the ratio $\Lambda/T_0 = 3.54$, as well as the polynomial parameterization of the Polyakov-loop potential. Below $k_{G_S,\text{crit}} = 0.882$, no chiral symmetry breaking occurs.