Can Dirac neutrinos destabilize $\mathcal{Z}_2$ domain wall network?

This paper demonstrates that if a $\mathcal{Z}_2$ symmetry responsible for generating light Dirac neutrino masses is spontaneously broken, it can radiatively induce the explicit breaking necessary to destabilize domain wall networks, thereby creating a predictable link between the Dirac neutrino mass scale and a detectable stochastic gravitational wave signal.

The Gist

The Cosmic "Wall" Problem and the Neutrino Solution

Imagine you are playing a massive, high-stakes game of "Split the Universe." In the very early stages of the Big Bang, a fundamental rule (a symmetry) was broken. This wasn't just a minor change; it was like a massive tectonic shift that created giant, invisible "walls" throughout space.

In physics, these are called Domain Walls.

The Problem: The Walls That Wouldn't Leave

Think of these domain walls like massive, indestructible curtains hanging across the entire universe. If these curtains are stable, they become incredibly heavy. Eventually, they would become so heavy that they would "overcrowd" the universe, pulling all the energy toward them and preventing stars, galaxies, and humans from ever forming.

For a long time, physicists have had a problem: if you have these walls, how do you get rid of them without just "cheating" (adding random math to make them disappear)?

The Discovery: The Neutrino "Demolition Crew"

This paper proposes a brilliant, natural solution. It turns out that the same tiny, ghostly particles responsible for giving neutrinos (the most elusive particles in existence) their mass are actually the ones that destroy these walls.

The Analogy: The Heavy Curtains and the Tiny Vibrations
Imagine those massive, universe-sized curtains (the Domain Walls) are held up by a perfect balance of pressure. To get rid of them, you don't need a giant wrecking ball; you just need a tiny, constant "nudge" to make one side of the curtain heavier than the other. Once one side is heavier, gravity pulls the curtain down, it collapses, and the "room" (the universe) is cleared.

The authors show that Dirac neutrinos—specifically the heavy particles that help create them—act like a microscopic "vibration" or a "nudge." Because of how these neutrinos interact with the universe, they create a tiny bit of extra pressure (a "bias") on one side of the wall.

This isn't a random nudge; it is a mathematical necessity built into the very fabric of how neutrinos get their mass. The "demolition crew" is already part of the blueprint!

The "Echo" of the Collapse: Gravitational Waves

When these massive cosmic walls finally collapse under that tiny neutrino nudge, they don't just vanish quietly. It’s like a giant building being demolished—it creates a massive, rumbling shockwave.

In space, these shockwaves are Gravitational Waves—ripples in the fabric of spacetime itself.

The paper makes a profound connection:

1. The Neutrino Mass tells us how heavy the "nudge" is.
2. The Nudge tells us when the walls will collapse.
3. The Collapse tells us how loud the "rumble" (the gravitational wave) will be.

Why This Matters

This is like finding a secret link between the smallest things we know (neutrinos) and the largest, most violent events in the history of the cosmos (the collapse of domain walls).

The authors suggest that upcoming "ears" in space—super-sensitive gravitational wave detectors like LISA or SKA—might actually "hear" these echoes. If we detect these specific ripples, it wouldn't just be a cool sound; it would be a smoking gun proving that neutrinos are exactly what we think they are and explaining how our universe survived its chaotic infancy to become the stable place it is today.

Technical Summary

This paper, titled "Can Dirac neutrinos destabilize $Z_2$ domain wall network?" by Borah, Paul, and Sahu, presents a theoretical framework that connects the origin of Dirac neutrino masses to the cosmological evolution of domain walls and the production of stochastic gravitational waves (GWs).

1. The Problem: The Domain Wall Problem

In many particle physics models, a discrete symmetry (such as $Z_2$) is spontaneously broken to explain certain phenomenological features (like generating neutrino masses). However, the spontaneous breaking of a discrete symmetry in the early Universe leads to the formation of domain walls (DWs). If these walls are stable, they quickly dominate the energy density of the Universe, which contradicts observations of the Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN).

Traditionally, physicists solve this by adding an "ad hoc" explicit breaking term (a "bias") to the scalar potential to make the walls unstable. However, such terms are usually introduced without a fundamental theoretical origin, breaking the predictive connection between the neutrino sector and the domain wall sector.

2. Methodology: Radiative Bias Generation

The authors propose a "self-biased domain wall" mechanism. They consider a Type-I Dirac seesaw model where:

• The Standard Model is extended by three generations of right-handed neutrinos ($\nu_R$), a real singlet scalar ($\eta$), and heavy vector-like singlet fermions ($N$).
• A $Z_2$ symmetry is imposed: $\nu_R$ and $\eta$ are $Z_2$-odd, while all other fields are even.
• The $Z_2$ symmetry is spontaneously broken when $\eta$ acquires a vacuum expectation value (VEV), $v_\eta$.

The Key Innovation: Instead of adding a bias term by hand, the authors show that the same heavy fermions ($N$) responsible for generating the light Dirac neutrino masses also generate an explicit $Z_2$-breaking term in the scalar potential through one-loop radiative corrections.

3. Key Contributions and Technical Results

The paper establishes a mathematical bridge between the neutrino mass scale and the gravitational wave signal:

• The Bias Term ($V_{bias}$): The authors derive that the radiative bias term scales with the heavy fermion mass ($m_N$) and the Yukawa coupling ($y_\eta$). Crucially, they show that $V_{bias}$ can be expressed in terms of the light neutrino mass ($m_\nu$).
• Scaling Laws: They find a profound scaling relationship:
  • The bias term scales inversely with the cube of the Dirac neutrino mass ($V_{bias} \propto m_\nu^{-3}$).
  • The resulting stochastic gravitational wave (GW) spectrum is proportional to the sixth power of the Dirac neutrino mass ($\Omega_{GW} \propto m_\nu^6$).
• Gravitational Wave Spectrum: The collapse of these "self-biased" walls releases energy as a stochastic GW background. The peak frequency ($f_{peak}$) and amplitude ($\Omega_{peak} h^2$) are determined by the seesaw scale ($m_N$), the VEV ($v_\eta$), and the Yukawa coupling ($y_\eta$).
• Dirac Leptogenesis: The authors demonstrate that the model can simultaneously explain the observed baryon asymmetry of the Universe through Dirac leptogenesis. In this process, CP-violating decays of $N$ create equal and opposite asymmetries in the left-handed and right-handed neutrino sectors, which are prevented from equilibrating.

4. Results and Observability

The paper maps out the parameter space to show that this model is highly testable:

• GW Detection: Depending on the seesaw scale, the GW signal can be probed by a wide range of upcoming experiments, including LISA, DECIGO, BBO, ET (Einstein Telescope), CE (Cosmic Explorer), and SKA (Square Kilometre Array).
• CMB Constraints: The model is consistent with $\Delta N_{eff}$ (dark radiation) constraints from the CMB. Even if the GW signal is not detected, the presence of light Dirac neutrinos could be probed via CMB-HD observations.
• Leptogenesis Window: They identify a specific region (requiring resonant enhancement of CP asymmetry) where the model successfully explains both the baryon asymmetry and produces a GW signal detectable by THEIA and SKA.

5. Significance

The significance of this work lies in its predictivity and theoretical elegance. By deriving the domain wall bias from the neutrino mass-generation mechanism itself, the authors remove the "ad hoc" nature of previous models. They establish a direct, non-trivial link between:

1. Neutrino Physics (the Dirac seesaw scale and mass).
2. Cosmology (the annihilation of domain walls and baryon asymmetry).
3. Gravitational Wave Astronomy (the specific frequency and amplitude of the stochastic background).

This provides a multi-messenger way to test the nature of neutrino masses using both particle physics experiments and gravitational wave observatories.