Gravitational Wave Production and Baryogenesis in a Simple Left-Right model

TL;DR

This work investigates gravitational wave production and electroweak baryogenesis in a minimal left-right symmetric model with two Higgs doublets and a singlet σ. By analyzing the finite-temperature effective potential, it reveals multi-step phase transition histories, including high-temperature electroweak breaking with strong first-order dynamics, which push the gravitational-wave peak frequencies to higher values than typical electroweak-scale transitions. The GW signal comprises bubble collisions, sound waves, and turbulence, with peak frequencies that may fall within the reach of next-generation detectors such as the Cosmic Explorer and Einstein Telescope. Baryogenesis is explored via CP violation sourced by a complex singlet ξ and transport equations across moving bubble walls, yielding viable η_B for benchmark points compatible with collider bounds. Overall, the results suggest that high-temperature left-right transitions can generate detectable gravitational waves and enable electroweak baryogenesis in a relatively simple scalar sector, with possible broader applicability beyond this specific model.

Abstract

The left-right model with the simplest Higgs structure has a $SU(2)_L$ doublet $H_L$, a $SU(2)_R$ doublet $H_R$, and a singlet $σ$ that couples to the doublets as $σ(|H_L|^2-|H_R|^2)$. The left-right symmetry has $H_L\leftrightarrow H_R$ and $σ\leftrightarrow-σ$. We study gravitational wave production and baryogenesis in the electroweak phase transitions in the model. For two benchmark points, $σ$ first gets a vev, followed by $H_R$ and then $H_L$. An interesting feature is that the vev of $H_L$ is initially much higher than its zero temperature value, leading to a more strongly first-order transition and higher frequency gravitational waves. An unusual benchmark point has the $σ$ vev at zero when the electroweak symmetry breaks. This results in both $H_L$ and $H_R$ vevs being equal and in the multi-TeV range. At a lower temperature, the $σ$ vev turns on, breaking the left-right symmetry and $H_L$ drops to its standard model value. Since the electroweak symmetry is broken at the multi-TeV scale, the frequency of gravitational waves will be much higher than usual. Baryogenesis is also discussed.

Figures (4)

• Figure 1: The vevs as a function of temperature for two benchmark points. The solid lines correspond to benchmark point 1 and the dashed line to benchmark point 2. Benchmark point 3 is very similar to benchmark point 2. At extremely high temperatures, the vev of the $\sigma$ is also zero in all cases considered.
• Figure 2: The critical temperature and the nucleation temperature for a typical set of parameters
• Figure 3: The gravitational wave spectrum for our benchmark points. Benchmark point 1 is the solid line, benchmark point 2 is the dashed line and benchmark point 3 is the dotted line. Note that since the electroweak transition temperature is much higher than in most models, the peak frequency is also substantially higher. CE and ET are the expected sensitivity of the Cosmic Explorer and Einstein Telescope, respectively.
• Figure 4: Feynman diagrams for generating the baryon asymmetry.