Gravitational Waves from First-Order Phase Transitions: LIGO as a Window to Unexplored Seesaw Scales

TL;DR

This work investigates a classically scale-invariant model in which Majorana neutrino masses and the Higgs potential arise radiatively after spontaneous breaking of scale invariance. The scale phase transition is shown to be strong first order with substantial supercooling, and careful accounting of vacuum energy reveals regions of parameter space where the transition cannot complete. For the viable points, the resulting stochastic gravitational wave background has peak frequencies in the $1$--$100$ Hz range and amplitudes around $\mathcal{O}(10^{-8})$, making it observable by current and upcoming gravitational wave detectors, notably LIGO in its O3 run. Since the new physics scale $v_s$ is above $10^7$ GeV, gravitational waves provide a crucial probe of this high-scale seesaw framework where collider access is impractical.

Abstract

Within a recently proposed classically conformal model, in which the generation of neutrino masses is linked to spontaneous scale symmetry breaking, we investigate the associated phase transition and find it to be of strong first order with a substantial amount of supercooling. Carefully taking into account the vacuum energy of the metastable minimum, we demonstrate that a significant fraction of the model's parameter space can be excluded simply because the phase transition cannot complete. We argue this to be a powerful consistency check applicable to general theories based on classical scale invariance. Finally, we show that all remaining parameter points predict a sizable gravitational wave signal, so that the model can be fully tested by future gravitational wave observatories. In particular, most of the parameter space can already be probed by the upcoming LIGO science run starting in early 2019.

Figures (6)

• Figure 1: Strength of the first-order scale phase transition in our model. (a) Temperature-dependent global minimum of the effective potential for the benchmark points in \ref{['tab:PT:benchmark']}. (b) Transition strength $v_c/T_c$ (color code) for the comprehensive, exemplary parameter scan presented in Ref. Brdar:2018vjq (cf. Table I and Figure 1 therein for details). All displayed points are fully consistent from the perspective of a zero-temperature analysis as discussed in \ref{['sec:nu_option']} and Ref. Brdar:2018vjq. However, only for parameter points within the red-shaded area the phase transition was found to actually complete. For further information on how this region was determined, we refer the reader to footnote \ref{['fn:PT:vcTc']} on page \ref{['fn:PT:vcTc']}. Note that the blue-shaded region is excluded since the effective potential becomes unstable at $\Lambda$.
• Figure 2: Reheating temperature $T_*$ (color code) in the $v_s$-$\tilde{B}$ plane. The plot explicitly demonstrates that $T_*$ only very mildly depends on $\tilde{B}:=32\pi^2 B$ and that it is well described by \ref{['eq:PT:TvacAna']}.
• Figure 3: Values of $f_\text{peak}$ (color code) presented in the $v_s$-$\tilde{B}$ plane. Generally, for larger $T_*$, the peak frequency increases as can be seen from \ref{['eq:peak']}. The peak frequency in our model ranges from $\mathcal{O}(1Hz)$ to $\mathcal{O}(100Hz)$.
• Figure 4: Stochastic gravitational wave spectra for the benchmark points BP1 and BP2 (see \ref{['tab:PT:benchmark']}) are shown together with the limits (LIGO 2016--2017) and future sensitivities (LIGO 2019--2020, LIGO 2022+, DECIGO, BBO, LISA) of selected observatories. Our model predicts values for $f_\text{peak}$ in the $\mathcal{O}(1Hz)$ to $\mathcal{O}(100Hz)$ range (see \ref{['fig:fpeak']}) with an associated peak energy density of order e-8. Hence, the majority of the parameter points can already be tested in the upcoming LIGO observing run. The displayed power-law integrated sensitivity curves were constructed according to Ref. Thrane:2013oya assuming $\text{SNR}_\text{thr}=10$ for space-based experiments, and $\text{SNR}_\text{thr}=2$ for LIGO, respectively. Further information can be found in the main text below \ref{['eq:SNR']}.
• Figure 5: In the figure, all the viable points in our parameter scan are shown. For a given phase of LIGO (color code) we indicate in the left (right) panel the points for which the signal-to-noise ratio SNR as defined in \ref{['eq:SNR']} exceeds $5$$(10)$. If more than one phase satisfy the requirement, the color corresponds to the earliest one.