Neutrino Mass, Vacuum Stability and Higgs Inflation with Vector-Like Quarks and a Single Right-Handed Neutrino

This paper proposes a Standard Model extension incorporating degenerate vector-like quarks and a single right-handed neutrino to simultaneously generate neutrino masses, ensure electroweak vacuum stability up to the Planck scale, and achieve successful Higgs inflation consistent with current observational data.

The Gist

Imagine the universe as a giant, delicate house of cards. For decades, physicists have been trying to figure out if this house is built on solid ground or if it's just barely holding together, waiting for a slight breeze to knock it over.

This paper, written by Canan Karahan, proposes a renovation plan for the Standard Model of physics (the blueprint of our universe) to fix three major structural problems at once:

1. Why neutrinos have mass (tiny ghost-like particles that shouldn't have weight).
2. Why the universe isn't collapsing (the "vacuum stability" problem).
3. How the universe expanded so fast at the beginning (cosmic inflation).

Here is the story of the renovation, explained through simple analogies.

The Three Problems

1. The Ghosts with Weight (Neutrino Mass)
In the original blueprint (the Standard Model), neutrinos were supposed to be weightless. But experiments show they have a tiny bit of mass. It's like finding out your house's ghosts actually have feet and can walk. The paper uses a "Type-I seesaw" mechanism to explain this. Imagine a seesaw where a heavy person on one end (a new, heavy particle) pushes a light person on the other end (the neutrino) up just enough to give it a tiny bit of mass.

2. The Wobbly Foundation (Vacuum Stability)
The most critical issue is the "Higgs field," which gives particles their mass. Think of the Higgs field as the foundation of our house. Current measurements suggest this foundation is "metastable." Imagine a ball sitting in a shallow dip on a hill. It looks stable, but if it gets a little push, it could roll down into a deep, dark valley, destroying the house (and the universe) in the process. Physicists want to know: Is the foundation solid, or is it about to collapse?

3. The Big Bang's Turbo Boost (Higgs Inflation)
The universe started with a massive, exponential expansion called inflation. The paper suggests the Higgs field itself was the engine that drove this expansion. But for the engine to work, the foundation (the Higgs potential) must be perfectly flat and stable at high energies. If the foundation is wobbly, the engine sputters, and inflation fails.

The Renovation Plan: Adding New Beams

To fix these issues, the author adds two new types of "bricks" to the universe's blueprint:

1. Vector-Like Quarks (VLQs): Think of these as heavy-duty steel beams. They are new particles that interact with the Higgs field. Their main job is to act as stabilizers. Just as adding steel beams to a wobbly bridge prevents it from collapsing, these quarks change the way the Higgs field behaves at high energies, keeping the "ball" in the safe dip and preventing it from rolling into the deep valley.

   • The Catch: If you add too many beams or make them too heavy, you might break the bridge in a different way. The paper calculates exactly how many beams (between 1 and 10) and how heavy they need to be to keep things stable.

2. A Single Right-Handed Neutrino (RHN): This is the heavy person on the seesaw mentioned earlier. It generates the mass for the light neutrinos. Interestingly, this particle also acts as a shock absorber. While the steel beams (VLQs) do the heavy lifting to stop the collapse, the RHN smooths out the ride. It ensures that the path the Higgs field takes as it goes up to the energy levels of the early universe is perfectly flat, allowing the "inflation engine" to run smoothly.

How They Tested the Plan

The author didn't just guess; they ran a complex simulation (a "Renormalization Group" analysis) to see how these new particles affect the universe from the moment of the Big Bang up to today.

• The "Goldilocks" Zone: They found that you can't just add any number of beams.

  • If you add too few (1 or 2), the foundation is still too wobbly.
  • If you add too many or make the beams too heavy, the physics breaks down (the theory becomes "non-perturbative," meaning the math stops working).
  • The Sweet Spot: The model works best if you add at least 4 of these new quark beams. With 4 or more, the foundation becomes absolutely solid, even if the weight of the top quark (another particle) varies slightly within experimental error.

• The Smooth Ride: When they included the Right-Handed Neutrino (the shock absorber) along with the quark beams, the path to the early universe became incredibly smooth. This allowed the Higgs field to act as a perfect inflation engine.

The Results: A House That Stands

When the author compared their renovated model against real-world data from telescopes (like Planck and ACT) that look at the Cosmic Microwave Background (the afterglow of the Big Bang):

• The Prediction: The model predicts specific patterns in the universe's expansion (called the spectral index and tensor-to-scalar ratio).
• The Match: These predictions fit perfectly with the latest data. The model suggests the universe expanded in a way that matches what we see today, with a very low "tensor-to-scalar ratio" (a specific type of cosmic ripple).

The Comparison: With vs. Without the Shock Absorber

The author also tested a version of the model without the Right-Handed Neutrino (just the steel beams).

• Without the RHN: The foundation is still stable, but the path to the early universe is bumpy. The predictions for the early universe's expansion vary wildly depending on exactly how many beams you use. It's less reliable.
• With the RHN: The combination of beams and the shock absorber creates a "sweet spot" where the predictions are stable and match the data perfectly, regardless of small changes in the number of beams.

Conclusion

In simple terms, this paper argues that the universe is likely built on a more complex foundation than we thought. By adding a specific set of heavy quark "beams" and a single heavy neutrino "shock absorber," we can explain why neutrinos have mass, why our universe didn't collapse, and how it expanded so rapidly at the beginning—all while matching the observations we have today. It's a minimal, elegant fix that solves three big mysteries with just a few new pieces.

Technical Summary

Technical Summary: Neutrino Mass, Vacuum Stability and Higgs Inflation with Vector-Like Quarks and a Single Right-Handed Neutrino

Problem Statement
The Standard Model (SM) of particle physics faces three critical theoretical challenges: the origin of non-zero neutrino masses, the metastability of the electroweak (EW) vacuum, and the lack of a viable mechanism for cosmic inflation. Specifically, with the measured Higgs boson mass ($m_h \approx 125$ GeV) and top-quark mass ($m_t \approx 172.56$ GeV), the renormalization-group (RG) evolution of the Higgs self-coupling ($\lambda_H$) drives it to negative values at scales around $10^{10}$ GeV, rendering the EW vacuum metastable. Furthermore, while Higgs inflation offers an economical solution to cosmic inflation by identifying the SM Higgs field as the inflaton, its viability is contingent upon the stability of the Higgs potential up to the inflationary scale (near the Planck scale). The SM alone fails to satisfy this stability condition.

Methodology
The authors investigate a minimal phenomenological extension of the SM, denoted as SM+(n)VLQ+RHN, which introduces two new fermionic sectors:

1. $n$ degenerate down-type isosinglet vector-like quarks (VLQs): These are color triplets with hypercharge $Y=-1/3$ and mass $M_D$. They interact via a Yukawa coupling $y_D$ to the third-generation SM quarks.
2. A single right-handed neutrino (RHN): A gauge singlet with a large Majorana mass $M_N$ and Yukawa coupling $y_N$, implementing the Type-I seesaw mechanism.

The analysis employs a two-loop Standard Model renormalization-group equation (RGE) framework, supplemented by one-loop contributions from the VLQs and the RHN. The study involves:

• RG Evolution: Solving coupled RGEs from the electroweak scale up to the Planck scale ($M_{Pl}$), with proper matching conditions at the mass thresholds $\mu = M_D$ and $\mu = M_N$.
• Parameter Space Scan: Fixing the RHN parameters to reproduce the observed light neutrino mass scale ($m_\nu \approx 0.05$ eV) via $M_N \approx 10^{14}$ GeV and $y_N \approx 0.42$. The remaining free parameters are the number of VLQs ($n$), their mass ($M_D$), and their Yukawa coupling ($y_D$).
• Constraints: The analysis respects experimental bounds from LHC searches (excluding $M_D \lesssim 1.5$ TeV) and electroweak precision data (constraining the mixing angle $\sin \theta_L \lesssim \mathcal{O}(10^{-2})$), as well as theoretical constraints on perturbativity ($|y_D| \lesssim 0.5$) and unitarity.
• Inflationary Analysis: Using the RG-improved Higgs potential in the metric formulation of non-minimal Higgs inflation, the authors compute inflationary observables ($n_s$ and $r$) and compare them with Planck-LB-BK18 and ACT-LB-BK18 data.

Key Contributions and Results

• Vacuum Stability Mechanism:

  • The VLQs play the dominant role in stabilizing the Higgs potential. Their contribution to the $\beta$-function of $\lambda_H$ is positive, counteracting the negative contribution from the top Yukawa coupling.
  • The RHN, while necessary for neutrino mass generation, contributes negatively to the $\beta$-function of $\lambda_H$, acting as a destabilizing agent.
  • Critical Findings:
    • For the full SM+(n)VLQ+RHN framework, absolute vacuum stability ($\lambda_{min} > 0$) up to the Planck scale is achieved only for $n \geq 4$ across all benchmark masses ($M_D = 1.5, 3.0, 5.0$ TeV) and for $n=3$ only at lower masses ($1.5, 3.0$ TeV).
    • The stability is robust against current experimental uncertainties in the top-quark mass ($m_t$) for $n \geq 4$.
    • In the SM+(n)VLQ limit (without RHN), the stabilizing effect is stronger, allowing stability for $n \geq 3$ (and even $n=2$ at $M_D=1.5$ TeV). However, this limit lacks the "smoothing" effect required for inflation.

• Higgs Inflation Predictions:

  • SM+(n)VLQ+RHN: The interplay between the stabilizing VLQ sector and the destabilizing RHN Yukawa coupling results in a remarkably smooth running of $\lambda(\mu)$ in the inflationary regime ($10^{15} - 10^{19}$ GeV). Consequently, the inflationary predictions for the spectral index ($n_s$) and tensor-to-scalar ratio ($r$) are only mildly sensitive to $n$ and $M_D$. The model predicts a low-$r$ regime ($r \sim 0.004 - 0.007$) that lies comfortably within the 68% confidence level of both Planck-LB-BK18 and ACT-LB-BK18 data.
  • SM+(n)VLQ (No RHN): Without the RHN, the running of $\lambda(\mu)$ exhibits stronger scale dependence. This leads to a broader spread in $(n_s, r)$ predictions that is highly sensitive to $n$ and $M_D$. Specifically, configurations with $n=2$ are excluded, and $n=3$ shows tension with Planck data at higher masses, though $n \geq 4$ remains consistent.

• Comparison of Frameworks:
  The paper explicitly contrasts the two scenarios to quantify the roles of the new sectors. The VLQs provide the necessary stabilization to prevent the potential from turning negative, while the RHN is crucial for smoothing the RG trajectory in the high-scale inflationary domain, thereby ensuring consistency with cosmological observations.

Significance and Claims
The authors claim that the SM+(n)VLQ+RHN framework represents a "phenomenologically minimalistic yet powerful approach" to simultaneously address three major open problems in particle physics and cosmology.

1. Unified Solution: It generates light neutrino masses via the Type-I seesaw mechanism, stabilizes the electroweak vacuum up to the Planck scale, and enables successful Higgs inflation.
2. Theoretical Consistency: The model remains consistent with current experimental constraints (LHC, electroweak precision) and theoretical requirements (perturbativity, unitarity) within well-defined regions of parameter space (specifically requiring $n \geq 4$ for robust stability).
3. Cosmological Viability: Unlike the SM+(n)VLQ limit, the inclusion of the RHN ensures that the inflationary observables are compatible with the latest high-precision CMB data (including the slight shift toward higher $n_s$ favored by ACT) without fine-tuning the number of VLQs or their masses.

The paper concludes that this two-particle extension offers a theoretically well-controlled realization of Higgs inflation that is robust against top-quark mass uncertainties and consistent with the current landscape of cosmological data.