⚛️ phenomenology

Leptogenesis via Resonant Sequential Dominance and TBC3 Mixing in a Type-I Seesaw Model

This paper proposes a "Resonant Sequential Dominance" framework within a Type-I seesaw model featuring a new TBC3 mixing ansatz and an $A_4 \times (Z_3)^4 \times (Z_2)^2$ symmetry, which successfully accommodates current neutrino oscillation data and explains the observed baryon asymmetry of the Universe via resonant leptogenesis with lightest right-handed neutrino masses between 0.13 and 230 TeV.

Original authors: Michael Fodroci, Teruyuki Kitabayashi

Published 2026-08-12

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Michael Fodroci, Teruyuki Kitabayashi

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, bustling party where everything is made of matter—stars, planets, you, me. But here's the weird part: physics says that when the party started, it should have been a perfect mix of matter and its evil twin, antimatter. If that had happened, they would have annihilated each other instantly, leaving nothing but a flash of light. The fact that we are here, surrounded by matter and almost no antimatter, is one of the universe's biggest mysteries. It implies that at some point, the rules of the party were slightly rigged to let matter win.

To figure out how this happened, scientists look at the smallest, most elusive guests at the party: neutrinos. These are ghostly particles that rarely interact with anything, yet they might hold the key to the mystery. The leading theory suggests that heavy, invisible cousins of these neutrinos (called right-handed neutrinos) decayed in the early universe, creating a tiny imbalance that eventually turned into all the matter we see today. This process is called "leptogenesis." However, for this to work, the heavy neutrinos need to have very specific properties, and their masses need to be just right—like tuning a radio to find a clear signal. If the signal is too weak or the frequency is off, the universe remains empty.

This paper, written by Michael Fodroci and Teruyuki Kitabayashi, is like a detective story trying to solve how to tune that radio. The authors propose a new way to arrange the "music" of the neutrinos, a method they call Resonant Sequential Dominance (RSD). Think of the standard way of arranging neutrino masses as a staircase where each step is much higher than the last. The authors suggest a different setup: imagine two steps that are almost exactly the same height, sitting right next to each other. This "degenerate" (nearly identical) setup creates a special resonance, like pushing a swing at just the right moment to make it go higher and higher. This resonance amplifies the tiny imbalance needed to create our matter-filled universe.

To make this work, the authors introduce a new mathematical recipe for how neutrinos mix, which they whimsically name TBC3. It's a bit like a new dance step that fits the current data perfectly. They show that if you use this dance step and the "two-step" mass setup, you can explain the observed properties of neutrinos without needing to fine-tune the universe with impossible precision. They even built a complete theoretical "playbook" (a Lagrangian) using a specific set of symmetries (like a secret code called $A_4 \times (Z_3)^4 \times (Z_2)^2$ ) that allows this scenario to exist naturally.

The most exciting part of their findings is the size of the heavy neutrinos needed to pull off this trick. The authors calculate that for this resonant mechanism to generate enough matter to fill the universe, the lightest of these heavy neutrinos must have a mass between 0.13 TeV and 230 TeV. This is a huge range, but it's significant because the lower end of that range is within the energy reach of the Large Hadron Collider (LHC), the world's most powerful particle accelerator. While the paper doesn't claim to have found these particles yet, it suggests that if they exist within this specific mass window, we might be able to spot them in future experiments. The authors also found that the tiny difference in mass between the two nearly identical heavy neutrinos (the "splitting") needs to be incredibly small, ranging from $2.45 \times 10^{-9}$ GeV to $4.31 \times 10^{-6}$ GeV, to keep the resonance humming just right.

In short, this paper doesn't prove that this specific scenario is the one true answer, but it demonstrates that it is a very viable and elegant possibility. It shows that by relaxing the strict rules of how neutrino masses are ordered, we can open up a new window to explain why we exist, all while sticking to the data we have today. It's a fresh, playful, yet rigorous approach to one of the oldest questions in cosmology: why is there something rather than nothing?

Technical Summary: Leptogenesis via Resonant Sequential Dominance and TBC3 Mixing in a Type-I Seesaw Model

Problem Statement
The observed baryon asymmetry of the Universe (BAU) and the smallness of neutrino masses are two major open questions in particle physics. While the Type-I seesaw mechanism naturally explains light neutrino masses via heavy right-handed (RH) Majorana neutrinos, standard models often suffer from a vast parameter space that limits predictive power. Sequential Dominance (SD) is a framework that reduces this complexity by imposing a texture on the Dirac mass matrix where specific RH neutrinos dominate the generation of specific light neutrino masses. However, standard SD typically relies on a hierarchical spectrum of RH neutrino masses ( $M_1 \ll M_2 \ll M_3$ ), which is incompatible with Resonant Leptogenesis (RL). RL requires at least two RH neutrinos to be nearly degenerate ( $M_1 \approx M_2$ ) to generate sufficient CP violation via resonant enhancement, yet maintaining the successful phenomenological features of SD (explaining mass hierarchies and mixing angles) under degenerate RH masses remains a challenge. Furthermore, recent experimental data, particularly the JUNO measurement of the solar mixing angle, has placed the Tri-Bi-Maximal (TBM) and standard Tri-Maximal (TM2) mixing ansätze in tension with observations, necessitating new mixing matrix proposals.

Methodology
The authors propose an extension of SD called Resonant Sequential Dominance (RSD). In this framework, the light neutrino mass hierarchy is generated not by the hierarchy of RH neutrino masses (which are degenerate, $M_1 \approx M_2 \ll M_3$ ), but solely through the hierarchy of Yukawa couplings.

TBC3 Mixing Ansatz: To address the tension with current neutrino oscillation data (specifically the solar angle $\theta_{12}$ ), the authors introduce a new mixing matrix ansatz termed TBC3. This ansatz is a second-order expansion around the TBM mixing matrix, parameterized by deviations in the solar ( $s$ ), atmospheric ( $a$ ), and reactor ( $r$ ) angles. The authors set $s = a = -\frac{1}{3\sqrt{3}}\lambda$ and $r = \frac{2}{3\sqrt{2}}\lambda$ , where $\lambda$ is the Cabibbo parameter. This choice aims to reproduce experimental mixing angles using simple ratios while maintaining unitarity within acceptable limits.
Phenomenological Search: Using King's Master Formula, the authors relate the low-energy observables (mixing angles, mass-squared differences, CP phases) to the elements of the Dirac mass matrix. They perform a $\chi^2$ analysis to search for "simple" values (integers, simple roots, and fractions) for the Dirac mass matrix elements and their complex phases that satisfy the TBC3 ansatz and current NuFIT global best-fit data.
Model Construction: An explicit Lagrangian is constructed based on the symmetry group $A_4 \times (Z_3)^4 \times (Z_2)^2$ . This symmetry dictates the field content (three RH neutrinos, flavons $\phi_i, \chi_i, \phi$ ) and their charge assignments, ensuring the required texture zeros and diagonal Majorana mass structures up to dimension-five operators.
Leptogenesis Calculation: The authors connect the phenomenological RSD parameters to the Lagrangian parameters. They solve coupled Boltzmann equations numerically to compute the lepton asymmetry ( $\eta_L$ ) and the resulting BAU ( $\eta_B$ ). They investigate the parameter space defined by the Yukawa coupling $y_{D1}$ , the cutoff scale $\Lambda$ , and the mass splitting parameter $x_\Delta$ (related to the degeneracy breaking $\Delta$ ).

Key Contributions

Resonant Sequential Dominance (RSD): The paper formalizes a framework where SD phenomenology is preserved despite degenerate RH neutrino masses, shifting the source of the mass hierarchy from the RH mass spectrum to the Yukawa coupling hierarchy.
TBC3 Ansatz: The proposal of a new mixing matrix ansatz that successfully fits current neutrino data (including the JUNO solar angle result) with a minimal number of parameters and simple mathematical structures.
Simple Dirac Textures: The identification of specific, simple Dirac mass matrix alignments (notably the "Simple $(\sqrt{2}, 1; 1, 2)$ Alignment") that yield 1 $\sigma$ agreement with all neutrino oscillation observables.
Explicit Symmetric Lagrangian: The construction of an $A_4 \times (Z_3)^4 \times (Z_2)^2$ -symmetric Lagrangian that realizes the RSD framework and admits resonant leptogenesis.
Parameter Space Constraints: A detailed numerical analysis establishing the viable ranges for the lightest RH neutrino mass and the necessary mass splitting to reproduce the observed BAU.

Results

Mixing Angles: The TBC3 ansatz, with the Simple $(\sqrt{2}, 1; 1, 2)$ alignment, predicts mixing angles $\theta_{12} \approx 33.95^\circ$ , $\theta_{13} \approx 8.57^\circ$ , and $\theta_{23} \approx 42.55^\circ$ , which are in 1 $\sigma$ agreement with NuFIT data (though $\theta_{23}$ is marginally within the 1 $\sigma$ range, a direct consequence of the ansatz's assumption of equal solar and atmospheric deviations).
BAU Generation: Numerical solutions of the Boltzmann equations demonstrate that the model can successfully generate the observed baryon asymmetry ( $\eta_B \approx 6.12 \times 10^{-10}$ ).
Mass Constraints: The analysis constrains the lightest RH neutrino mass ( $m_{N1}$ ) to the range:
$0.13 \text{ TeV} \leq m_{N1} \leq 230 \text{ TeV}$
This range depends on the Yukawa coupling $0.1 \leq y_{D1} \leq 1$ and the cutoff scale $100 \text{ TeV} \leq \Lambda \leq 419 \text{ TeV}$ .
Mass Splitting: To achieve the required CP asymmetry, the mass splitting between the degenerate RH neutrinos must satisfy:
$2.45 \times 10^{-9} \text{ GeV} \leq x_{\Delta, \text{min}} \leq 4.31 \times 10^{-6} \text{ GeV}$
The lower bound ensures viability across the entire allowed parameter space, while the upper bound corresponds to the most extreme parameter set.

Significance and Claims
The paper claims to demonstrate that phenomenological model construction based on Sequential Dominance can be successfully extended to scenarios with degenerate RH neutrino masses, thereby accommodating Resonant Leptogenesis without sacrificing the model's ability to explain neutrino mass hierarchies and mixing angles. By introducing the TBC3 ansatz, the authors provide a viable alternative to TBM/TM2 that aligns with the latest precision data from JUNO and NuFIT.

The authors emphasize that their approach is an "indirect model-building" strategy; they do not propose a fundamental symmetry that naturally produces the specific "Simple" alignments found, nor do they explain the origin of the RH neutrino mass splitting. However, they establish a concrete link between low-energy observables and high-energy Lagrangian parameters, showing that a specific range of RH neutrino masses (accessible potentially at the LHC, though collider phenomenology is not analyzed) can explain the BAU. The work serves as a proof-of-concept that RSD is a consistent and predictive framework for connecting neutrino oscillation data to the baryon asymmetry of the Universe.

More like this