⚛️ phenomenology

Probing axion in the DFSZ model

This paper proposes an extended DFSZ axion model incorporating right-handed neutrinos and new scalars, demonstrating that the Peccei-Quinn transformation becomes independent of the Higgs mixing angle and that the resulting coupling modifier for the trilinear Higgs self-coupling remains consistent with current experimental constraints for specific mass and vacuum expectation value parameters.

Original authors: H. N. Long, N. H. T. Nha

Published 2026-07-07

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CC BY 4.0

Original authors: H. N. Long, N. H. T. Nha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, complex machine. For decades, physicists have been trying to fix a specific glitch in this machine called the "Strong CP puzzle." It's a bit like trying to tune a radio that keeps picking up static no matter how you turn the dial. The "axion" is a proposed particle that acts like a magical tuning knob to silence that static.

This paper explores a specific blueprint for how this axion works, called the DFSZ model, but with a major upgrade: the authors added a new set of "right-handed neutrinos" (heavy, invisible particles) to the mix.

Here is a breakdown of their findings using simple analogies:

1. The New "Tuning Knob" (The PQ Transformation)

In previous versions of this model, the axion's behavior depended on a complicated mix of two different settings (like adjusting both volume and bass simultaneously).

The Paper's Claim: By adding those new heavy neutrinos, the authors found that the axion's behavior now depends on only one setting: the "charge" of a single, invisible scalar particle (called $\phi$ ).
The Analogy: Think of the old model as a car with a steering wheel that was connected to the engine and the brakes in a confusing way. The new model is like a car where the steering wheel only controls the direction, making the driving much simpler and more predictable.

2. The Cast of Characters (The Particles)

The model introduces four new types of particles, which the authors describe as a family of "scalars" (particles related to the Higgs boson that gives things mass):

The Charged Higgs ( $H^\pm$ ): A heavy, electrically charged particle.
The CP-odd Scalar ( $A$ ): A neutral particle that behaves differently under mirror reflections.
The CP-even Scalars ( $h$ and $S$ ): Two neutral particles. One is the familiar Higgs boson we already know (the "SM-like" one), and the other is a new, heavier sibling ( $S$ ) weighing in at about 220 GeV (roughly 200 times heavier than a proton).
The Inflaton ( $\Phi$ ): A super-heavy particle that acts like a cosmic "starter motor" for the universe's rapid expansion (inflation) right after the Big Bang. It is incredibly massive, far beyond what our current particle colliders can reach.

3. No Mixing Up the Signals

One of the biggest headaches in these theories is that the axion often gets "mixed up" with another particle called the Goldstone boson (which is like a ghost particle that gives mass to the Z boson).

The Paper's Claim: The authors used a special mathematical method (unitary matrices) to organize these particles.
The Analogy: Imagine trying to listen to two different radio stations that are bleeding into each other. The authors' method is like installing a perfect filter that ensures the axion signal stays on its own channel and never interferes with the Goldstone boson channel. This makes the math much cleaner.

4. How the Axion Talks to Others

The paper explains how this axion interacts with other matter:

The "Whisper" (Derivative Couplings): The axion talks to fermions (matter particles like electrons and quarks) through a "whisper" that depends on how fast the axion is moving. This is a standard way axions interact.
The "Handshake" (Yukawa-like Interactions): The axion also has a direct "handshake" with matter, similar to how the Higgs boson gives mass to particles.
The Ratio: The paper confirms that the ratio of how the axion talks to light (photons) versus how it talks to the strong nuclear force is exactly 8/3. This matches a specific, well-known version of the theory called "DFSZ Type I."

5. The "Goldilocks" Zone for New Physics

The authors tested their model against current experimental data from the Large Hadron Collider (LHC). They looked at a specific parameter called $\kappa_\lambda$ , which measures how strongly the Higgs boson interacts with itself.

The Finding: They found a "sweet spot" where the model works perfectly with current data.
The Numbers: If the new heavy particles (the charged Higgs and the CP-odd scalar) have masses around 150 GeV (roughly the weight of a Higgs boson), and the "vacuum expectation value" (a measure of the energy field) is just a few GeV, the model fits.
The Result: In this specific range, the model predicts a new heavy scalar particle ( $S$ ) with a mass of about 220 GeV. The authors show that this prediction stays within the safety limits set by current experiments (ATLAS and CMS).

Summary

The authors have built a refined version of the axion theory that includes heavy neutrinos. This version simplifies the math, separates the axion from confusing background noise, and predicts a new family of heavy particles. Crucially, they showed that if these new particles exist with masses around 150–220 GeV, the theory remains consistent with everything we currently know about the Higgs boson.

What the paper does NOT claim:

It does not claim to have discovered the axion yet.
It does not claim to solve the "muon g-2" problem or "neutrino mixing" in this specific text (though it mentions these as general motivations for the model in the introduction, the results focus on the Higgs and axion couplings).
It does not propose any medical or clinical applications.

Technical Summary: Probing Axion in the DFSZ Model with Right-Handed Neutrinos

Problem Statement
The Peccei–Quinn (PQ) mechanism remains the primary solution to the strong CP problem. The Dine–Fischler–Srednicki–Zhitnitsky (DFSZ) model, an extension of the Standard Model (SM) involving two Higgs doublets and a singlet scalar, was originally proposed in the 1980s under the assumption of massless neutrinos. However, modern neutrino oscillation data necessitates the introduction of right-handed neutrinos ( $N_R$ ) to generate neutrino masses via the seesaw mechanism. The integration of these heavy neutrinos into the DFSZ framework requires a re-evaluation of the PQ transformation properties, the scalar spectrum, and the resulting axion couplings. Furthermore, the model must be tested against current experimental constraints on Higgs self-couplings and scalar masses.

Methodology
The authors construct a DFSZ-type model augmented by three singlet heavy right-handed neutrinos ( $N_R$ ). The particle content includes the SM fermions, two Higgs doublets ( $H_u, H_d$ ), a complex scalar singlet ( $\phi$ ), and the new $N_R$ .

Symmetry and Transformations: The authors define the $U(1)_{PQ}$ symmetry by assigning charges to all multiplet components. Unlike previous treatments where PQ charges might depend on mixing angles, this work demonstrates that the PQ transformation depends solely on the PQ charge of the scalar singlet ( $PQ_\phi$ ).
Scalar Sector Diagonalization: The scalar potential is expanded around vacuum expectation values (VEVs). The authors employ unitary matrices to diagonalize the charged, CP-odd, and CP-even scalar sectors. A critical methodological step is ensuring the physical fields are orthogonal, specifically verifying that there is no mixing between the axion ( $a$ ) and the Goldstone boson ( $G_Z$ ).
Mass Spectrum Calculation: The mass matrices for charged scalars, CP-odd scalars, and CP-even scalars are derived. The authors analyze the mass eigenstates, identifying the SM-like Higgs ( $h$ ), a heavy CP-even scalar ( $S$ ), a charged Higgs ( $H^\pm$ ), a CP-odd scalar ( $A$ ), and a superheavy inflaton ( $\Phi$ ).
Coupling Analysis: The paper calculates axion couplings to fermions, distinguishing between derivative couplings (anomaly-induced) and Yukawa-like interactions arising from the scalar potential. The ratio of the electromagnetic anomaly coefficient ( $E$ ) to the QCD anomaly coefficient ( $N$ ) is computed.
Phenomenological Constraints: The trilinear Higgs self-coupling modifier ( $\kappa_\lambda$ ) is calculated as a probe of new physics. The authors scan the parameter space (specifically $\lambda_u$ , $t_\lambda = \lambda_d/\lambda_u$ , $m_A$ , and $m_{H^\pm}$ ) to determine regions consistent with current experimental bounds from ATLAS and CMS.

Key Contributions and Results

PQ Transformation Independence: The study establishes that with the inclusion of right-handed neutrinos, the PQ transformation depends only on $PQ_\phi$ and is independent of $\sin(\arctan(v_u/v_d))$ and $\cos(\arctan(v_u/v_d))$ . This simplifies the charge assignment compared to previous literature.
Orthogonality of States: By using unitary matrices for diagonalization, the authors confirm that the axion $a$ and the Goldstone boson $G_Z$ do not mix. This ensures a clean separation of the axion state from the electroweak sector.
Axion Couplings: The model is identified as a DFSZ I type, characterized by the ratio $E/N = 8/3$ . The axion-fermion interactions are shown to consist of two distinct types: Yukawa-like interactions (proportional to fermion masses) and anomaly-induced derivative couplings. Notably, there is no tree-level coupling between the axion and the photon.
Scalar Mass Spectrum:
- The model predicts a superheavy inflaton $\Phi$ with mass $\sim 10^{11}$ GeV.
- New scalars ( $H^\pm$ , $A$ , $S$ ) are predicted at the electroweak scale.
- For specific parameter choices ( $m_A \approx 130$ GeV, $m_{H^\pm} \approx 155$ GeV, $\sin \beta \approx 0.0688$ ), the model yields a SM-like Higgs mass of $\approx 125$ GeV and a heavy CP-even scalar $S$ with a mass around $220$ GeV.
Higgs Self-Coupling: The coupling modifier $\kappa_\lambda$ is calculated. The authors find that for parameter regions where $m_A \sim 130$ GeV, $m_{H^\pm} \sim 155$ GeV, and $\lambda_u \approx 0.03-0.035$ , the value of $\kappa_\lambda$ falls within the current experimental bounds ( $-0.71 < \kappa_\lambda < 6.1$ at 95% C.L.). Specifically, the model is consistent with data when $t_\lambda$ is in the range of approximately 3.9 to 4.9.

Significance and Claims
The paper claims that the proposed DFSZ model with right-handed neutrinos offers a unified framework addressing several open problems in particle physics and cosmology without violating current experimental constraints. The authors highlight that the model simultaneously addresses:

Neutrino Mass and Mixing: Via the Type-I seesaw mechanism mediated by heavy $N_R$ .
The Muon $(g-2)$ Anomaly: The introduction of $N_R$ is noted to provide a solution to this discrepancy.
Cosmological Inflation: The superheavy scalar $\Phi$ serves as the inflaton.
Higgs Physics: The model provides a consistent extension of the Higgs sector with new scalars at the TeV scale.

The authors conclude that the model is a viable candidate for new physics, particularly noting that the derived coupling modifier $\kappa_\lambda$ is consistent with recent LHC data. They suggest that the specific parameter space identified (with new scalars around 150–220 GeV and a specific vacuum structure) warrants further investigation in future collider phenomenology.