Synergy between measurements of the gravitational wave and the triple Higgs coupling in probing first order phase transition

TL;DR

The paper investigates how jointly measuring the triple-Higgs coupling and the stochastic gravitational-wave background can probe the nature of the electroweak phase transition in scale-invariant $O(N)$ scalar extensions. It shows that CSI models generically yield a large $hhh$ deviation of about $\frac{\Delta\lambda_{hhh}}{\lambda^{SM}_{hhh}}=\frac{2}{3}$ and a strongly first-order transition, leading to GW spectra detectable by future space-based detectors. By comparing CSI and non-CSI scenarios, the work demonstrates that GW observations—especially with Caprini-style fits for sound waves and turbulence—can distinguish underlying EWSB dynamics even when collider signals are similar. The results underscore a synergistic pathway to narrow down viable BSM implementations of EWSB through complementary collider and GW data.

Abstract

Probing the Higgs potential and new physics behind the electroweak symmetry breaking is one of the most important issues of particle physics. In particular, nature of electroweak phase transition is essential for understanding physics at the early Universe, such that the strongly first order phase transition is required for a successful scenario of electroweak baryogenesis. The strongly first order phase transition is expected to be tested by precisely measuring the triple Higgs boson coupling at future colliders like the International Linear Collider. It can also be explored via the spectrum of stochastic gravitational waves to be measured at future space-based interferometers such as eLISA and DECIGO. We discuss complementarity of both the methods in testing the strongly first order phase transition of the electroweak symmetry in models with additional isospin singlet scalar fields with and without classical scale invariance. We find that they are synergetic in identifying specific models of electroweak symmetry breaking in more details.

Figures (9)

• Figure 1: The contours of the mass of the Higgs boson $m_h$ and $\varphi_c/T_c$ in the $(N, m_S)$ plane in the CSI $O(N)$ model.
• Figure 2: Predicted values of $\alpha$ and $\tilde{\beta}$ in the CSI $O(N)$ models (red) and $O(N)$ models without CSI for $\sqrt{\mu_S^2}=0~{\text{GeV}}$ (gray).
• Figure 3: The efficiency factor $\kappa_v^{}$ as a function of $v_b^{}$ for $\alpha=0.01, 0.1$ and $1$. The cases for $v_b^{}=c_s^{}$ and $v_b^{}=v_J^{}$ are plotted with dotted lines.
• Figure 4: GW spectra in the CSI $O(N)$ models (top frames) and $O(N)$ models without CSI with $\Delta\lambda_{hhh}^{}/\lambda_{hhh}^{{\text{SM}}}=2/3 (\simeq 70\%)$ (bottom frames) for $v_b^{}=0.95$ (left) and $v_b=0.2^{}$ (right). The black curves correspond to the contributions from the sound waves (solid) and turbulence (dashed) for $N=1,4,12$ and $60$ (left) for $N=1,4$ and $12$ (right) from the bottom.
• Figure 5: GW spectra in the $O(N)$ models without CSI with $\sqrt{\mu_S^2}=100~{\text{GeV}}$ and $\Delta\lambda_{hhh}^{}/\lambda_{hhh}^{{\text{SM}}}=2/3 (\simeq 70\%)$ for the runaway case ($v_b^{}=1$). The black curves correspond to the contributions from the sound waves (solid), bubble collision (dotted) and turbulence (dashed) for $N=4,12$ and $60$ from the bottom.