Gravitational waves from the first order phase transition of the Higgs field at high energy scales

TL;DR

The paper analyzes whether the Standard Model Higgs could have experienced a first-order phase transition at a high energy scale due to couplings with a new physics scalar, and whether such a transition would generate gravitational waves detectable by future observatories. Using a general scalar potential that includes the NP field and possible singlet extensions, the authors compute the finite-temperature effective potential and evaluate bubble nucleation dynamics, deriving GW spectra from bubble collisions and turbulence via parameters $\alpha$ and $\beta$. They find that a SM-like Higgs sector yields GWs that are too weak to detect, but singlet-extended scenarios can produce observable signals, especially for large numbers of singlets $N_S$ or for small Higgs quartic coupling $\lambda_H$, with peak frequencies around $\sim$1 Hz and amplitudes reaching $\Omega_{\rm GW}\gtrsim10^{-15}$ in favorable cases. These results suggest that GW observations could probe high-scale new physics through Higgs-sector dynamics, and motivate studying other scalar-field phase transitions that couple to the Higgs.

Abstract

In a wide class of new physics models, there exist scalar fields that obtain vacuum expectation values of high energy scales. We study the possibility that the standard model Higgs field has experienced first order phase transition at the high energy scale due to the couplings with these scalar fields. We estimate the amount of gravitational waves produced by the phase transition, and discuss observational consequences.

Figures (11)

• Figure 1: Schematic picture of the zero temperature potential. First, both $H$ and $\phi_{\rm NP}$ sit at the origin. The phase transition labeled as "1" in the figure occurs at $T=T_{H}^{\rm PT}$. Then the next phase transition, labeled as "2" in the figure, occurs at $T=T_{\phi_{\rm NP},H\neq 0}^{{\rm PT}}$.
• Figure 2: The temperature dependence of $\lambda_H/g^2$. The black-dashed line corresponds to $\lambda_H/g^2 = 0.18$. Each color corresponds to $(m_h,m_t) = (124.77,174.32)$ (blue), $(125.09,173.34)$ (red), and $(125.41,172.36)$ (yellow). The left end points correspond to the transition temperature at which $\lambda_H / g^2 = 0.18$.
• Figure 3: $\alpha$ as a function of $T_*$. The Higgs and top masses are taken to be the same as in Fig. \ref{['fig_lHrun_SM']}.
• Figure 5: The peak position and amplitude of the GW spectrum for bubble collision (solid lines) and turbulence (dotted lines). The Higgs and top masses are taken to be the same as in Fig. \ref{['fig_lHrun_SM']}.
• Figure 6: $\alpha$ with $f_{\rm peak}=1$ Hz as a function of $N_S$. Solid lines correspond to bubble collision, while dotted lines correspond to turbulence. $\lambda_{SH}=1$ (blue), $1.5$ (red) and $2$ (yellow).