Gravitational waves from flavoured SU(2) early-universe phase transitions

TL;DR

This work investigates gravitational waves from early-universe phase transitions in flavoured SU(2) gauge theories, focusing on a breaking pattern driven by a real scalar and potentially accompanied by leptoquarks. The authors deploy dimensional reduction to construct a finite-temperature effective potential, analyze nucleation with bounce solutions, and couple this to steady-state hydrodynamics to predict the gravitational-wave spectra, highlighting the necessity of order-one gauge couplings for a strong first-order transition. They show that including leptoquarks significantly widens the testable parameter space and that the Einstein Telescope offers excellent prospects to detect flavoured SU(2) phase-transition signals across a broad energy range up to around $10^7$ GeV. The results underscore the potential of gravitational-wave observations to probe high-scale flavour dynamics that are otherwise inaccessible to collider or flavour experiments, providing a complementary window into the origin of fermion masses and the structure of Yukawa couplings.

Abstract

Flavourful extensions of the Standard Model aimed at explaining its fermionic mass structure typically rely on symmetries, broken at high-energy scales far beyond the reach of foreseeable direct collider searches. We illustrate, using a $SU(2)$ flavour gauge group, that the breaking of these symmetries up to scales as high as $10^7$ GeV could generate a gravitational-wave signal potentially observable by future observatories. We use dimensional reduction techniques to obtain the finite-temperature effective potential and study the possible first-order phase transitions. We match these transitions to steady-state hydrodynamical solutions in order to determine the corresponding gravitational-wave spectra. We observe that order-one gauge couplings are always required for a first-order phase transition to occur. On the other hand, adding leptoquarks (as an example of particles that are typically present in a complete flavour theory) significantly extends the testable parameter space. We find excellent prospects at the Einstein Telescope for future gravitational-wave detection of flavoured $SU(2)$ early-universe phase transitions.

Figures (15)

• Figure 1: Scalar quartic coupling in the ultra-soft theory at the soft matching scale as function of the initial 4d flavour gauge couplings for $\lambda_\phi = 0.025$, for two different 3d to 4d matching scales. We set $v_0 = 50$ TeV.
• Figure 2: The various mass scales relevant for the 3d soft theories. We set $v_0 = 50$ TeV.
• Figure 3: (Left) Evolution of the 4d broken vacuum localisation at the critical temperature from the complete NNLO estimation of DRalgo. (Right) the 4d effective potential at the critical temperature, with the increasing barrier for $g_f = \{1,1.5,2 \}$, $\lambda_{\phi}=0.025$, $\lambda_s = 0.5$, and $\lambda_{\phi s} = 0.25$. While $T_c$ is equivalent in the 3d and 4d theory, the rescaling between 3d and 4d results in a rescaled VEV in 4d. We set $v_0=50$ TeV.
• Figure 4: (Left) Evolution of the critical temperature from the complete NNLO estimation of DRalgo. (Right) for the 4d VEV, we plot the corresponding ratio of VEV over critical temperature indicating the strength of the FOPT.
• Figure 5: Evolution of $\alpha_N$ with $g_f$ for each of the benchmark points ($v_0=50$ TeV).