Testing the type-II seesaw mechanism with gravitational waves

TL;DR

This paper proposes using high-frequency gravitational waves as an indirect probe of the type-II seesaw mechanism, focusing on graviton bremsstrahlung emitted during the out-of-equilibrium decays of the Higgs triplet $\Delta$ in the early Universe. It develops the type-II seesaw model with a $Y=1$ triplet, derives the Higgs-triplet decay widths to leptons and Higgs bosons, and analyzes the thermal history of $\Delta$ via Boltzmann equations for its comoving abundance and energy density. The authors compute the gravitational-wave production through the collision terms for $\Delta \to LLg$ and $\Delta \to HHg$, solve the Boltzmann equation for the GW energy density, and obtain the present spectrum $\Omega_{GW} h^2(f)$, showing a strong dependence on $M_\Delta$ and $v_\Delta$ (via BRs) and a characteristic $\propto M_\Delta^2$ scaling when BRL = BRH. They conclude that, with future high-frequency resonant-cavity detectors, this GW signal could provide a unique avenue to test the seesaw mechanism and gain insight into neutrino mass generation at high scales.

Abstract

Traditional seesaw mechanisms provide an elegant theoretical framework for explaining the small yet non-zero masses of neutrinos. Nevertheless, they face significant experimental challenges, primarily because the energy scale associated with the seesaw mechanism is too high to be directly probed in terrestrial experiments. In this paper, we explore the gravitational waves (GWs) generated via graviton bremsstrahlung during the decay of seesaw particles in the early Universe. Specifically, we compute the GW spectrum resulting from the decay of the Higgs triplet within the type-II seesaw model. Our results demonstrate that the resulting GW spectrum depends sensitively on the mass of the Higgs triplet and its couplings to the Standard Model Higgs doublet and the left-handed lepton doublet. The detection of such a high-frequency GW background could offer a unique experimental window into the seesaw mechanism and provide indirect evidence for its validity.

Figures (9)

• Figure 1: Left: Decay widths of the Higgs triplet as functions of $v_\Delta$ for $M_\Delta = 10^{14}\,\text{GeV}$. Right: Branching ratios for Higgs-triplet decays into leptons (BRL) and into Higgs bosons (BRH) as functions of $v_\Delta$ for the same mass. The vertical dashed line in the left panel marks the value of $v_\Delta$ at which the total decay width is minimized; this value coincides with the intersection of BRL and BRH in the right panel.
• Figure 2: Evolution of the comoving energy densities for the Higgs triplet and radiation, with $M_\Delta = 10^{14} \text{ GeV}$ and $\zeta=10^{-4}$. The red solid line represents the comoving energy density of the Higgs triplets, $Y_\rho ^\Delta$, while the black horizential line represents that of radiation, $Y_\rho ^{SM}$.
• Figure 3: Feynman diagrams for graviton bremsstrahlung in the decay of Higgs triplets. The left two diagrams are for the process $\Delta \to HHg$, and the right two diagrams are for the process $\Delta \to LLg$.
• Figure 4: Left: Gravitational wave spectrum produced by the Higgs decay channel for different values of $M_\Delta$ and $\zeta$. Right: Gravitational wave spectrum produced by the leptonic decay channel for different values of $M_\Delta$ and $\zeta$. The red and blue lines correspond to $M_\Delta = 10^{14} \text{ GeV}$ and $M_\Delta = 10^{15} \text{ GeV}$, respectively. The solid and dashed lines represent $\zeta = 10^{-3}$ and $\zeta = 10^{-4}$, respectively.
• Figure 5: Gravitational wave spectrum produced by the decay of Higgs triplets with different values of $M_\Delta$ and $\zeta$, assuming equal branching ratios for the leptonic and Higgs channels, i.e., $\text{BRL} = \text{BRH} = 1/2$. The red and blue lines correspond to $M_\Delta = 10^{14} \text{ GeV}$ and $M_\Delta = 10^{15} \text{ GeV}$, respectively. The solid and dashed lines represent $\zeta = 10^{-3}$ and $\zeta = 10^{-4}$, respectively. The sensitivity curves for the resonant-cavity experiments are depicted with dotted lines.