Flavon assisted low scale leptogenesis

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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

The Big Picture: Two Unsolved Mysteries

Imagine the universe as a giant, complex machine. Physicists have built a "User Manual" called the Standard Model that explains how most of the machine works. But there are two huge missing pages in the manual:

Why do neutrinos have mass? (The manual says they should be weightless, but experiments show they have a tiny bit of weight.)
Why is there more matter than antimatter? (When the universe began, it should have created equal amounts of matter and antimatter, which would have annihilated each other, leaving nothing but light. Instead, we have a universe full of stars, planets, and people. Something tipped the scales.)

The Old Solution: The "Heavy" Problem

For decades, the leading theory to fix both problems was the Seesaw Mechanism.

The Analogy: Imagine a seesaw. On one side, you have the light neutrinos we see. On the other side, you have invisible, super-heavy "Right-Handed Neutrinos" (RHNs).
The Catch: To make the light side so light, the heavy side has to be astronomically heavy (trillions of times heavier than a proton).
The Problem: If these heavy particles are that massive, we can never build a machine big enough to find them. It's like trying to find a specific grain of sand on a beach the size of the galaxy. Also, to create the matter/antimatter imbalance, these heavy particles usually need to be "twins" with almost identical masses, which feels like a weird coincidence that needs extra explaining.

The New Idea: The "Flavon" Helper

This paper proposes a clever workaround. Instead of needing super-heavy twins, let's introduce a new character: a Flavon.

What is a Flavon? In particle physics, "flavor" refers to the different types of particles (like electron, muon, tau). A Flavon is a special field (like an invisible force field) that gives particles their specific "flavor" and mass. Think of it as a mold that shapes the clay of the universe.
The Twist: The authors realized that this Flavon field can act as a matchmaker or a catalyst.

How It Works: The Party Analogy

Imagine the heavy Right-Handed Neutrinos (RHNs) are two party guests, N2 and N3.

The Old Way: For the universe to get its matter/antimatter imbalance, N2 and N3 had to be identical twins (same mass) and decay (leave the party) at the exact same time in a very specific way. This was hard to arrange.
The New Way (Flavon Assisted): Enter the Flavon (S).
1. The Secret Door: The Flavon opens a new secret door at the party. Now, the heavier guest (N3) can decay not just into normal particles, but also into the lighter guest (N2) plus the Flavon itself ( $N3 \to N2 + S$ ).
2. The Chaos: This new path creates a bit of chaos (CP violation). It messes up the perfect balance between matter and antimatter in a way that the old "twin" scenario couldn't do as easily.
3. The Result: Because of this extra path, the heavy particles don't need to be identical twins anymore. They can have different masses, and they can be much lighter (around the TeV scale, which is heavy for a particle but light enough that we might actually build a machine to find them in the future).

The Specific Model: A "One-Flavon" Solution

The authors tested this idea using a specific mathematical model (based on a symmetry group called $A_4$ ).

The Setup: In this model, the Flavon is already there to give the neutrinos their masses. It's like the mold that was already shaping the clay.
The Discovery: They found that this same Flavon naturally does the job of the "matchmaker" described above. It connects two specific neutrinos, opens the new decay channel, and helps create the matter/antimatter imbalance.
Why it's cool: It's efficient. You don't need to invent a whole new universe of particles; you just use the one you already have (the Flavon) to solve two problems at once.

The Results: Is it Realistic?

The authors ran the numbers (simulations) to see if this actually works.

The Good News: Yes! They found a wide range of settings where this model successfully explains:
1. The tiny masses of the neutrinos we observe.
2. The specific way neutrinos mix (oscillate).
3. The exact amount of matter in the universe today.
The Constraints: The model has to play by the rules of other experiments. For example, the Flavon can't be too heavy or too light, or it would have been detected by the Large Hadron Collider (LHC) or mess up the properties of the Higgs boson.
The Sweet Spot: They found that if the heavy neutrinos are around 200 GeV to 5 TeV (which is within reach of current or near-future particle colliders), and the Flavon is in a specific mass range, everything clicks into place.

Summary

Think of this paper as finding a multi-tool in a toolbox.

Old View: We needed a giant, invisible hammer (super-heavy neutrinos) to fix the universe, but we couldn't find it.
New View: We realized the Flavon (a tool we already knew existed for a different job) can also act as a wrench. By using the Flavon to help the neutrinos decay in a new way, we can explain why we exist without needing super-heavy, perfectly identical twins.

This makes the theory much more "testable." Instead of waiting for a machine the size of a galaxy, we might be able to find evidence for this theory in the next generation of particle accelerators.

1. Problem Statement

The Standard Model (SM) fails to explain the origin of neutrino masses and the observed baryon-antibaryon asymmetry of the Universe (BAU). While the Type-I seesaw mechanism with heavy Right-Handed Neutrinos (RHNs) addresses both, the traditional implementation requires RHN masses at extremely high scales ( $O(10^9)$ – $O(10^{13})$ GeV), making them inaccessible to current or foreseeable experiments.

Low-scale leptogenesis scenarios (e.g., Resonant Leptogenesis or ARS leptogenesis) can operate at the TeV scale but typically suffer from a significant theoretical drawback: they require a highly degenerate mass spectrum of RHNs to enhance CP violation via resonant effects. This degeneracy often lacks natural justification within specific flavor models.

The paper addresses the question: Can one achieve successful low-scale leptogenesis at the TeV scale without requiring a highly degenerate RHN mass spectrum, while maintaining consistency with neutrino oscillation data?

2. Methodology and Model Framework

Theoretical Proposal

The authors propose that flavon fields—scalar fields introduced in flavor-symmetry models to generate RHN masses via non-zero vacuum expectation values (VEVs)—can naturally serve as the scalar singlet $S$ required to facilitate low-scale leptogenesis.

Mechanism: The interaction term $S N_I N_J$ (where $I \neq J$ ) opens new decay channels ( $N_I \to N_J S$ ).
Effect: These new channels enhance the departure from thermal equilibrium and introduce additional sources of CP violation at the one-loop level, bypassing the need for mass degeneracy.

Specific Model Implementation

To demonstrate this, the authors utilize a specific flavor-symmetry neutrino mass model based on the group $A_4 \times Z_2^1 \times Z_2^2 \times Z_3^2$ (from Ref. [38]), chosen for its ability to reproduce the TM1 (Trimaximal 1) mixing pattern, which is consistent with current experimental data (unlike the ruled-out Tri-Bimaximal pattern).

Key Features of the Model:

RHN Structure: Three RHNs ( $N_1, N_2, N_3$ ) are introduced. $N_1$ is a singlet under the flavor symmetry and decouples from the others. $N_2$ and $N_3$ form a doublet structure.
Flavon Role: A single flavon field $S$ $S$ (denoted as $\xi$ $ξ$ in the original reference) acquires a VEV ( $v_S$ $v_{S}$ ).
- It generates a mixing term $\Delta M$ between $N_2$ and $N_3$ , rotating the mass basis and modifying the Dirac mass matrix to achieve TM1 mixing.
- Crucially, this same field $S$ couples to $N_2$ and $N_3$ via the interaction $\alpha_0 S N_2 N_3$ .
Simplification: The model is minimal in that only one flavon field plays the dual role of generating RHN masses/mixing and acting as the mediator for leptogenesis. Furthermore, it couples only to two RHNs ( $N_2$ and $N_3$ ), simplifying the Boltzmann equation analysis.

Computational Approach

The authors solve the Boltzmann equations to track the evolution of particle abundances and asymmetry.

Processes Included:
- Standard decays: $N_I \leftrightarrow L_\alpha H$ .
- New decay channel: $N_3 \to N_2 S$ .
- $\Delta L = 2$ scattering processes mediated by $S$ : $N_I N_J \to HH$ .
CP Asymmetry Calculation: The total CP asymmetry ( $\epsilon_3$ ) for $N_3$ decays is calculated including standard contributions plus new vertex and self-energy diagrams mediated by the flavon $S$ .
Constraints: The parameter space is constrained by:
- Neutrino oscillation data (mass squared differences, mixing angles, TM1 pattern).
- Higgs physics (mixing angle $|\sin \theta| \lesssim 0.3$ ).
- Invisible Higgs decay limits ( $BR(h \to SS) \leq 0.23$ ).
- Perturbativity and vacuum stability of the scalar potential.

3. Key Contributions

Identification of Flavons as Leptogenesis Mediators: The paper establishes that flavon fields, ubiquitous in flavor models, are ideal candidates for the scalar singlet $S$ needed to enable low-scale leptogenesis without mass degeneracy.
Realization in a Phenomenologically Viable Model: Unlike previous illustrative examples that predicted the now-disallowed Tri-Bimaximal (TBM) mixing, this work applies the mechanism to a model that naturally yields the TM1 mixing pattern, consistent with the measured non-zero $\theta_{13}$ .
Demonstration of Viability without Degeneracy: The authors prove that successful baryogenesis is achievable at the TeV scale with hierarchical RHN masses, provided the flavon-mediated decay channel is active.
Comprehensive Parameter Analysis: The study provides a detailed scan of the parameter space ( $M_2, M_3, m_S, \beta, \alpha_0$ ) under both Normal Ordering (NO) and Inverted Ordering (IO) of neutrino masses, incorporating all relevant experimental constraints.

4. Results

Baryon Asymmetry Generation: The model successfully reproduces the observed baryon asymmetry ( $Y_B \approx 8.69 \times 10^{-11}$ ) across a wide range of parameters.
Mass Scales:
- Normal Ordering (NO): Successful leptogenesis is possible for $M_2$ $M_{2}$ as low as $\sim 200$ GeV.
  - At low $M_2$ ( $\sim 200$ GeV), the viable region for the flavon mass $m_S$ is low ($1 $–$ 100$ GeV).
  - As $M_2$ increases (e.g., to 5 TeV), the viable region shifts to higher flavon masses ( $m_S \gtrsim 300$ GeV).
- Inverted Ordering (IO): Similar qualitative behavior is observed, but the viable parameter space is more restricted compared to the NO case.
Coupling Constraints:
- The trilinear coupling $\beta$ (from the term $\beta S |H|^2$ ) is critical. For $M_2 \sim 2$ TeV and $|\alpha_0| \sim 10^{-3}$ , $\beta$ values around $10^3$ GeV are sufficient.
- The mixing angle between the Higgs and the flavon is constrained to $|\sin \theta| \lesssim 0.3$ , which is satisfied within the viable regions.
Kinematic Requirement: The decay $N_3 \to N_2 S$ must be kinematically allowed ( $m_S < M_3 - M_2$ ), which is naturally satisfied in the successful regions.

5. Significance

Bridging Flavor and Cosmology: The work provides a concrete link between flavor symmetry models (designed to explain neutrino mixing) and the cosmological origin of matter. It suggests that the fields responsible for flavor structure are also the key to generating the matter-antimatter asymmetry.
Testability: By lowering the RHN mass scale to the TeV range (specifically down to $\sim 200$ GeV in the NO case) without requiring fine-tuned mass degeneracy, the scenario becomes potentially testable at future colliders (e.g., HL-LHC, FCC-ee) and through precision Higgs measurements.
Model Independence: While demonstrated in a specific $A_4$ model, the authors argue that the underlying mechanism (flavons acting as $S$ ) is applicable to a broad class of flavor-symmetry models, offering a general pathway to low-scale leptogenesis.

In conclusion, the paper demonstrates that flavon-assisted leptogenesis is a robust and natural mechanism to explain the baryon asymmetry of the Universe at accessible energy scales, resolving the tension between the need for low-scale physics and the constraints of flavor models.