Gravitational waves at aLIGO and vacuum stability with a scalar singlet extension of the Standard Model

TL;DR

This work investigates whether a minimal SM extension with a real gauge-singlet scalar can realize a strongly first-order phase transition at a nucleation temperature $T_N$ in the range $10^7$–$10^8$ GeV, producing a stochastic gravitational-wave background potentially detectable by aLIGO during its O5 run. By constructing a finite-temperature effective potential, solving for degenerate minima at the critical temperature $T_C$ and computing $T_N$ from bounce solutions, the authors estimate the gravitational-wave signal via the envelope approximation, focusing on peak frequency $f_0$ and amplitude $\Omega_{\rm GW}$. They perform a Monte Carlo scan of high-scale parameters to identify three benchmark points that yield observable GW while maintaining vacuum stability and SM-like phenomenology, and they discuss the role of a positive threshold correction to the SM quartic in stabilizing the potential up to high scales. The study also reveals a Goldilocks region for the PT strength, $2.3 \lesssim \gamma \lesssim 3$, that optimizes detectability. Overall, the results show that aLIGO O5 could probe high-energy physics tied to vacuum stability through a high-scale first-order phase transition driven by a singlet scalar.

Abstract

A new gauge singlet scalar field can undergo a strongly first-order phase transition (PT) leading to gravitational waves (GW) potentially observable at aLIGO and simultaneously stabilize the electroweak vacuum. aLIGO (O5) is potentially sensitive to cosmological PTs at $10^7$-$10^8$ GeV, which coincides with the requirement that the singlet scale is less than the Standard Model (SM) vacuum instability scale, which is between $10^8$ GeV and $10^{14}$ GeV. After sampling its parameter space, we identify three benchmark points with a PT at about $T\approx 10^7$ GeV in a gauge singlet extension of the SM. We calculate the nucleation temperature, order parameter, characteristic timescale, and peak amplitude and frequency of GW from bubble collisions during the PT for the benchmarks and find that, in an optimistic scenario, GW from such a PT may be in reach of aLIGO (O5). We confirm that the singlet stabilizes the electroweak vacuum whilst remaining consistent with zero-temperature phenomenology as well. Thus, this scenario presents an intriguing possibility that aLIGO may detect traces of fundamental physics motivated by vacuum stability at an energy scale that is well above the reach of any other experiment.

Figures (4)

• Figure 1: The effective potential (i.e., free energy) for benchmark SSM II, shown above, below and at the critical temperature, $T_C$, at which the minima are degenerate, and at the nucleation temperature, $T_N$.
• Figure 2: Running of the Higgs quartic $\lambda$ in the SM and for our solutions in the SSM. All lines correspond to $m_h \simeq 125\,\text{GeV}$.
• Figure 3: Peak amplitudes and frequencies of GW for our SSM benchmark points from our approximate numerical calculation of $\beta / H_N$ (squares), with uncertainty represented by varying between $\beta / H_N = 1$ and $\beta / H_N = 200$ (lines). The shaded regions indicate LIGO sensitivities during various phases of runningTheLIGOScientific:2016wyqThrane:2013oya. All lines intersect the sensitivity of aLIGO (LIGO running phase O5).
• Figure 4: Scatter plots of solutions in the SSM that exhibit strongly first-order PT at $T_C \in ( 10^7,10^8) \,\text{GeV}$, acceptable weak-scale phenomenology, and no Landau poles below the GUT scale. For the benchmark points shown, in addition, we checked that the PT results in GW signatures are potentially within reach of aLIGO (O5).