Linking Axions, the Flavor Problem, and Neutrino Masses through a Flavored Peccei-Quinn Symmetry

This paper proposes a Flavored Peccei-Quinn model that unifies the explanation of quark flavor textures, the strong CP problem, and neutrino masses via a type-I seesaw mechanism, while predicting phenomenological signatures such as intermediate scalar resonances and specific axion-photon couplings constrained by current experimental data.

The Gist

Imagine the universe as a giant, complex machine built by a master engineer (Nature). For decades, physicists have been trying to understand the blueprints of this machine, specifically how the tiny gears (particles) get their weights and how they spin.

This paper is like a new, unified instruction manual that tries to fix three major "bugs" in the machine's design all at once, using a clever trick involving a hidden symmetry called the Peccei-Quinn (PQ) symmetry.

Here is the breakdown of what the authors did, using everyday analogies:

1. The Three Big Problems

The authors are trying to solve three distinct mysteries that have plagued physicists for years:

• The Strong CP Problem (The "Broken Compass"): In the world of subatomic particles, there's a rule that says certain forces should behave the same whether you look at them in a mirror or not. But mathematically, the universe should be broken in a way that violates this mirror rule. Yet, experiments show it isn't. It's like having a compass that should point North but keeps pointing East, yet somehow, the needle stays perfectly still. The "Axion" is the proposed fix—a tiny, invisible particle that acts like a self-correcting mechanism to force the compass back to North.
• The Flavor Problem (The "Weight Distribution"): Why is the top quark (a heavy particle) so heavy, while the electron is so light? Why do they mix in specific ways? It's like a piano where the keys are supposed to have specific weights, but the current design requires us to manually glue weights onto each key to make it work. The authors want a design where the weights come naturally from the structure of the piano itself.
• The Neutrino Mass Mystery (The "Ghost Weights"): Neutrinos are ghostly particles that barely have any mass. We know they have some mass, but we don't know why it's so tiny.

2. The Solution: A "Flavored" Symphony

The authors propose a model where these three problems are solved by the same underlying structure. Think of the universe as an orchestra.

• The Old Way: Usually, physicists treat the Axion (the compass fix), the particle weights (flavor), and the neutrino ghosts as separate sections of the orchestra, each needing its own conductor.
• The New Way (This Paper): The authors suggest there is only one conductor (the Flavored PQ Symmetry) directing the whole orchestra.
  • They introduce four different types of "Higgs" fields (imagine these as different types of musical instruments or tuning forks) instead of just the one we usually talk about.
  • They also add two "singlet" fields (hidden tuning forks) and some extra heavy particles.

3. How It Works: The "Texture" of the Machine

The magic happens because of how these extra tuning forks vibrate (their "Vacuum Expectation Values").

• The Recipe: The authors use a specific mathematical pattern called a "five-zero texture." Imagine a spreadsheet where most cells are empty (zero). By filling in only five specific cells with numbers, they can perfectly predict the weights of all the quarks (the building blocks of matter) and how they mix.
• The Connection: Because the "Axion" and the "Neutrino" both get their existence from the same hidden tuning fork (the singlet field $S_2$), their masses are linked.
  • Analogy: Imagine the Axion is a child and the Neutrino is a parent. In this model, the child's height (mass) is directly determined by the parent's height. If you know how heavy the neutrino is, you can calculate how heavy the axion must be, and vice versa. This creates a direct "family tree" link between two seemingly unrelated particles.

4. The "Ghost" at the LHC (The 95 GeV Signal)

One of the most exciting parts of the paper is how it explains recent rumors from the Large Hadron Collider (LHC).

• The Rumor: Scientists have seen a faint "glitch" or excess of light (diphotons) at a specific energy level (95 GeV). It's like hearing a faint, mysterious note in a song that the standard sheet music doesn't explain.
• The Explanation: The authors' model naturally predicts a new, light particle (a scalar boson) sitting right at that 95 GeV energy level.
• The Trick: Usually, adding so many new particles to fix the Axion problem makes them all super heavy (too heavy to be seen at the LHC). However, the authors found a special "sweet spot" in the math (by adjusting specific interaction terms) that allows one of these new particles to stay light enough to be the "ghost" seen at the LHC, while the others remain hidden or heavy.

5. The Safety Check

Before publishing, they had to make sure their new machine didn't break the laws of physics as we know them.

• Flavor Constraints: They checked if their model would cause particles to change into other particles in forbidden ways (like a proton turning into a pion too easily). They found that their specific "recipe" keeps these dangerous changes suppressed.
• Axion Hunting: They checked if their predicted Axion would have been caught by current experiments looking for dark matter. They found a "safe zone" where their Axion is light and weak enough to hide from current detectors but heavy enough to solve the Strong CP problem.

The Bottom Line

This paper is a "Grand Unified Theory" for three specific problems. It suggests that:

1. The reason particles have different weights is the same reason the Axion exists.
2. The reason neutrinos are so light is tied to the same mechanism that fixes the Strong CP problem.
3. The mysterious 95 GeV signal seen at the LHC might actually be one of the new particles predicted by this theory.

It's a bold attempt to replace a messy, patched-up machine with a sleek, elegant design where every part serves multiple purposes. If the LHC finds that 95 GeV particle and future experiments find the specific type of Axion they predict, this model could become the new standard for understanding the universe's hidden architecture.

Technical Summary

Here is a detailed technical summary of the paper "Linking Axions, the Flavor Problem, and Neutrino Masses through a Flavored Peccei–Quinn Symmetry" by Giraldo, Rojas, and Salazar.

1. Problem Statement

The paper addresses three fundamental open questions in particle physics simultaneously:

1. The Strong CP Problem: Why the QCD vacuum angle $\theta$ is effectively zero, despite being a free parameter in the Standard Model (SM).
2. The Flavor Problem: The origin of the hierarchical structure of fermion masses and the specific texture of the Cabibbo–Kobayashi–Maskawa (CKM) mixing matrix.
3. Neutrino Masses: The mechanism generating the tiny masses of neutrinos.

Additionally, the authors aim to explain recent experimental anomalies at the LHC, specifically the 95 GeV diphoton excess and the 125 GeV Higgs boson, within a unified framework. They note that standard Axion models (like DFSZ) often require large vacuum expectation values (VEVs) for the Peccei–Quinn (PQ) breaking scale ($f_a \sim 10^9$ GeV), which typically pushes scalar masses to the TeV scale or higher, making them incompatible with light scalar resonances observed at the LHC. The challenge is to construct a model that accommodates a light axion, realistic flavor textures, and light scalar states ($\sim 100$ GeV) without excessive fine-tuning.

2. Methodology and Model Construction

A. Particle Content and Symmetry

The authors propose an extension of the Standard Model featuring a Flavored Peccei–Quinn (FAM) symmetry ($U(1)_{PQ}$). The particle content includes:

• Four Higgs Doublets ($\Phi_{1,2,3,4}$): Necessary to generate the specific Yukawa textures required for the flavor structure.
• Two Complex Scalar Singlets ($S_{1,2}$): Responsible for breaking the global $U(1)_{PQ}$ symmetry. $S_2$ breaks PQ at a high scale, while $S_1$ interacts with the doublets.
• Right-Handed Neutrinos ($\nu_R$): To implement a Type-I seesaw mechanism.
• A Vector-like Quark ($Q$): A singlet under the SM gauge group but charged under $U(1)_{PQ}$, essential for anomaly cancellation and generating the PQ breaking scale.

B. Flavor Structure (Texture Zeros)

The model enforces five texture zeros in the quark mass matrices ($M_U$ and $M_D$) via the $U(1)_{PQ}$ charge assignments.

• The mass matrices are assumed to be Hermitian.
• The specific texture allows the quark masses and CKM mixing angles to be reproduced using Yukawa couplings of order unity, significantly improving naturalness compared to the SM where Yukawas span many orders of magnitude.
• The flavor structure is determined by the hierarchy of VEVs: $v_4 \ll v_1, v_2 \ll v_3 \ll v_{s2}$.

C. Scalar Potential and Mass Spectrum

The authors construct a general scalar potential compatible with the symmetries, including quadratic, quartic, and specific trilinear interactions (dimension-3 terms).

• Key Innovation: They demonstrate that by carefully choosing the trilinear terms (specifically parameters $K_3, F_1, F_2$), it is possible to decouple the heavy scalar states (associated with the high PQ breaking scale) from the light spectrum.
• This allows the model to predict a light CP-even scalar ($H_1$) near 95 GeV and a SM-like Higgs ($H_2$) at 125 GeV, despite the large $f_a$.
• The spectrum includes 6 CP-even, 4 CP-odd (one being the axion), and 3 charged scalar pairs.

D. Neutrino Mass Generation

The model implements a Type-I seesaw mechanism.

• The Majorana mass term for right-handed neutrinos arises from the coupling to the singlet $S_2$: $M_N \propto \langle S_2 \rangle$.
• The Dirac mass term arises from the coupling to the doublet $\Phi_3$ (SM-like VEV).
• This creates an intrinsic link between the neutrino mass scale and the axion decay constant ($f_a$).

3. Key Contributions and Results

A. Resolution of the "Light Scalar vs. High Scale" Tension

The paper successfully demonstrates that a Flavored PQ model can accommodate light scalar resonances ($\sim 100$ GeV) required to explain LHC diphoton excesses, even with a high PQ breaking scale ($f_a \sim 10^{15}$ GeV). This is achieved through specific trilinear couplings in the scalar potential that suppress the mixing between the heavy singlet sector and the light doublet sector.

B. Unification of Axion and Neutrino Physics

A major theoretical contribution is the derivation of a direct relationship between the axion mass ($m_a$) and the neutrino mass scale.

• Since $f_a \propto v_{s2}$ and the heavy neutrino mass $M_N \propto v_{s2}$, the light neutrino mass $m_\nu \propto v_{SM}^2 / v_{s2} \propto v_{SM}^2 / f_a$.
• Consequently, $m_\nu \propto m_a$.
• The authors derive a bound: $|x_{s2} \frac{(det Y^\nu)^{2/3}}{(det Y^N)^{1/3}} m_a| \leq 5.1 \times 10^{-9}$ eV (for Normal Ordering), linking cosmological neutrino mass limits directly to the axion mass parameter space.

C. Phenomenological Viability

• Flavor Constraints: The model is tested against Flavor-Changing Neutral Currents (FCNCs). The dominant constraints come from rare meson decays, specifically $K^\pm \to \pi^\pm a$. The model's specific PQ charge assignments suppress dangerous tree-level FCNCs, satisfying bounds from NA62, CLEO, and Belle.
• Axion-Photon Coupling: The model is checked against experimental limits on the axion-photon coupling ($g_{a\gamma}$) from haloscopes (ADMX), helioscopes (CAST), and astrophysical observations (Horizontal Branch stars). The authors identify regions of parameter space where the model is consistent with all current limits.
• Diphoton Excess: The light scalar $H_1$ (mass $\approx 95$ GeV) couples to photons via loops of charged fermions. Its small mixing with the SM-like Higgs ($\Phi_3$) allows it to reproduce the observed signal strength of the 95 GeV excess without violating the precision measurements of the 125 GeV Higgs.

4. Significance and Conclusion

This work provides a unified theoretical framework that connects three distinct sectors of particle physics:

1. Strong CP: Solved via the axion.
2. Flavor: Explained via texture zeros enforced by PQ charges, leading to natural $\mathcal{O}(1)$ Yukawa couplings.
3. Neutrino Masses: Generated via a seesaw mechanism tied to the PQ breaking scale.

Significance:

• Predictive Power: The model reduces the number of free parameters by linking the axion mass, neutrino masses, and flavor textures.
• Phenomenological Relevance: It offers a concrete explanation for the 95 GeV diphoton anomaly, a persistent feature in LHC data, within a well-motivated extension of the SM.
• Naturalness: It resolves the tension between high-scale axion models and low-energy collider phenomenology, showing that light scalars can exist naturally in PQ models without fine-tuning the entire potential, provided specific trilinear terms are present.

The authors conclude that future collider measurements (LHC Run 3, HL-LHC), flavor experiments, and dedicated axion searches will be crucial in testing the specific parameter space of this Flavored Axion Model.