Confinement transition to gravitational waves in the one-flavor $SU(4)$ Hyper Stealth Dark Matter theory

Abstract

The thermodynamics of the $SU(4)$ gauge theory with a single flavor of fundamental quarks is analyzed on the lattice with dynamical fermion simulations, which is the low-energy sector of a realistic, strongly-interacting dark matter model -- the Hyper Stealth Dark Matter. The gravitational wave spectrum from the first-order confinement transition in the early universe is further calculated, where the effect of the dark sea quarks, which decrease the interface tension in the effective potential of the Polyakov loop, is shown numerically to lower the gravitational wave amplitude.

Figures (15)

• Figure 1: The histogram $h(\bar{L})$ for the averaged Polyakov loop $\bar{L}$ at $\beta_c$ with $\hat{m}_q=0.4$ and $N_s=16,24,32$ from top left to bottom. Errorbar is suppressed.
• Figure 2: The location of the minimum $\bar{L}_0$ for $N_s=16,24,32$ from top left to bottom. $\hat{m}_q=0.1$ does not exhibit a discontinuous jump for $N_s=32$, implying a crossover, whose $\beta_c$ is determined by the largest derivative $d\bar{L}_0/d\beta$.
• Figure 3: The dimensionless constrained effective potential $\bar{V}'\equiv\bar{V}/T^4$ along the real axis at $\beta_c$. $\hat{m}_q=0.1,0.2,0.3,0.4$ from top left to bottom right.
• Figure 4: The peak amplitude $h^2\Omega_{\rm peak}$ and frequency $f_{\rm peak}$, compared against near-future detectors' sensitivity, taken from Ref. Schmitz:2020syl.
• Figure 5: (Left) $M_B/T_c$ and (Right) $(T_*-T_c)\sqrt{t_0}$ as functions of $M_B\sqrt{t_0}$. In the right panel, points with equal $M_B\sqrt{t_0}$ are horizontally displaced for visibility, and colors and markers are varied as in Fig. \ref{['fig:sensitivity']}.