⚛️ phenomenology

Non-resonant Flavoured leptogenesis with aligned two-Higgs doublet model and right-handed neutrinos

This paper demonstrates that non-resonant flavoured leptogenesis can successfully generate the observed baryon asymmetry of the universe with lightest heavy neutrino masses between 10 TeV and 100 TeV within an aligned two-Higgs doublet model augmented by two right-handed neutrinos, where the combined Yukawa structures of both scalar doublets and weak washout in specific flavour directions play essential roles.

Original authors: Km Pranjali, Indrani Chakraborty

Published 2026-10-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Km Pranjali, Indrani Chakraborty

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

The universe we inhabit is made almost entirely of matter, yet the laws of physics suggest that the Big Bang should have produced equal amounts of matter and antimatter. When these two opposites meet, they annihilate each other, leaving behind only pure energy. If the early universe had been perfectly balanced, everything would have vanished, and stars, planets, and people would never have existed. Instead, a tiny, mysterious imbalance occurred, leaving a surplus of matter that formed everything we see today. Scientists have long searched for the mechanism that tipped the scales, a process that could explain why we are here. One leading theory involves the behavior of heavy, invisible particles that existed in the first moments of the cosmos, decaying in a way that favored matter over antimatter. This process, known as leptogenesis, relies on the idea that these particles decayed while the universe was still cooling, creating a slight excess of leptons—a family of particles that includes electrons—which was later converted into the excess of protons and neutrons that make up our world.

A recent study by researchers at the Jaypee Institute of Information Technology in India explores a specific version of this story, testing whether a particular arrangement of particles and forces could successfully generate the observed amount of matter without requiring a rare, fine-tuned coincidence. The researchers focused on a model that extends the standard understanding of particle physics by adding two new types of heavy particles and a second type of Higgs field, a force-carrying field that gives other particles their mass. In this framework, the two Higgs fields are carefully aligned so that they do not cause certain forbidden reactions that experiments have never seen. The team used powerful computer simulations to track how these heavy particles would have behaved as the universe cooled, specifically looking at a mass range between 10,000 and 100,000 times the mass of a proton. They found that this setup can indeed produce the correct amount of matter-antimatter imbalance, but only because of a subtle interplay between different types of particles and how they interact with the surrounding heat of the early universe.

The key to this success lies in how the researchers treated the different "flavors" of the particles involved. In the early universe, the heavy particles decayed into lighter particles that come in three distinct varieties, much like the three types of electric charge found in nature. Previous studies often treated these varieties as a single group, but the researchers in this study realized that at the temperatures they were investigating, these varieties act as separate entities. They solved a complex set of equations to follow the evolution of each variety individually. Their calculations showed that the heavy particles created an imbalance in all three varieties, but the universe's environment acted like a filter, washing away the excess in two of the varieties while leaving the third one largely untouched. This surviving imbalance became the primary source of the matter we see today. The study demonstrates that the unique structure of their model, with its two Higgs fields and aligned interactions, provides the necessary ingredients to create this imbalance without needing the heavy particles to be nearly identical in mass, a condition that would have been required in other, more constrained theories.

The researchers were particularly interested in whether this process could work without a "resonant" boost, a scenario where the heavy particles must have almost exactly the same mass to amplify the effect. By running their simulations across a wide range of masses, they confirmed that the observed amount of matter can be generated even when the heavy particles have significantly different masses, as long as the difference is not too large. They identified specific combinations of parameters—such as the strength of the interactions and the relative masses of the particles—that satisfy all known experimental limits, including strict rules about how often certain rare particle decays occur. The study also checked that the model remains mathematically consistent and does not break down under the extreme conditions of the early universe. The results indicate that the observed matter-antimatter asymmetry is a natural outcome of this specific theoretical framework, provided the heavy particles fall within the 10,000 to 100,000 mass range and the interactions between them follow the aligned pattern described.

This work offers a compelling alternative to theories that rely on extreme fine-tuning, suggesting that the universe's matter surplus could be a robust feature of a slightly more complex particle landscape. The researchers found that the success of this mechanism depends heavily on the hierarchical nature of the "washout" effects, where the environment of the early universe selectively erases the imbalance in some particle types while preserving it in others. This selective survival is what ultimately determines the final amount of matter. The study concludes that while the heavy particles must be relatively close in mass to avoid the resonant regime, they do not need to be identical, and the specific arrangement of the Higgs fields plays a crucial role in enabling the process. By mapping out the allowed regions of this theoretical landscape, the authors have shown that a non-resonant, flavor-dependent leptogenesis is a viable explanation for the existence of our matter-dominated universe, grounded in a model that respects current experimental boundaries and theoretical consistency.

Technical Summary: Non-resonant Flavoured Leptogenesis in an Aligned Two-Higgs Doublet Model

Problem Statement
The observed matter-antimatter asymmetry of the universe, quantified by the baryon-to-photon ratio $\eta_B \approx 6.12 \times 10^{-10}$ , cannot be explained within the Standard Model (SM) due to insufficient CP violation and the inability of the SM to generate non-zero light neutrino masses. While the Type-I see-saw mechanism with heavy right-handed neutrinos (RHNs) offers a pathway to both neutrino mass generation and leptogenesis, standard analyses often rely on resonant enhancement (requiring nearly degenerate neutrino masses) to achieve the observed asymmetry at the TeV scale. Furthermore, conventional single-Higgs doublet models face constraints regarding Flavor Changing Neutral Currents (FCNCs). This work investigates whether a non-resonant, flavoured leptogenesis scenario can successfully generate the observed baryon asymmetry within an Aligned Two-Higgs Doublet Model (A2HDM) augmented with two RHNs, specifically in the mass range of 10 TeV to 100 TeV.

Methodology
The authors construct a theoretical framework extending the SM with a second scalar doublet and two heavy gauge-singlet RHNs ( $N_1, N_2$ ).

Model Structure: The model employs the Aligned Two-Higgs Doublet Model (A2HDM) to eliminate tree-level FCNCs by aligning the Yukawa coupling matrices of the two doublets in flavor space via a complex alignment parameter $\xi_\nu$ . This introduces additional sources of CP violation.
Neutrino Mass Generation: Light neutrino masses are generated via the Type-I see-saw mechanism. The Dirac Yukawa couplings are reconstructed using the Casas-Ibarra (CI) parametrization to ensure consistency with experimental neutrino oscillation data (fixing mixing angles and mass-squared differences, assuming one massless active neutrino).
Constraints: The parameter space is rigorously filtered against theoretical perturbativity bounds ( $|Y| < \sqrt{4\pi}$ ), current neutrino oscillation data, and the experimental upper limit on the charged lepton flavor violating (cLFV) process $\mu \to e\gamma$ ( $Br < 4.2 \times 10^{-13}$ ).
Leptogenesis Formalism: Given the heavy neutrino mass range ( $10^4 - 10^5$ GeV), the analysis operates in the fully flavoured regime ( $T < 10^9$ GeV), where quantum coherence between lepton flavors is lost. The authors solve a system of coupled Boltzmann equations for the heavy neutrino abundance and individual flavor asymmetries ( $Y_{\Delta \alpha}$ for $\alpha = e, \mu, \tau$ ).
CP Asymmetry Calculation: Unlike single-doublet models, the CP asymmetry ( $\epsilon_{1\alpha}$ ) receives contributions from interference terms involving both Higgs doublets ( $\Phi_1$ and $\Phi_2$ ) and their respective Yukawa couplings ( $Y^1$ and $Y^2$ ). The calculation includes tree-level decays, one-loop vertex corrections, and self-energy corrections.
Numerical Analysis: An exhaustive scan is performed over the multi-dimensional parameter space (masses $M_{1,2}$ , alignment parameters, $\tan\beta$ , and CI parameters). The evolution of asymmetries includes decay, inverse decay, $\Delta L = 1$ scattering, and spectator effects. The final baryon asymmetry is derived from the surviving $B-L$ asymmetry via sphaleron conversion.

Key Contributions

Dual Yukawa Contribution: The paper demonstrates that in the A2HDM framework, both Yukawa structures associated with the scalar doublets contribute to the CP asymmetry. The complex alignment parameter $\xi_\nu$ provides an additional source of CP violation distinct from the standard Type-I see-saw scenario.
Non-Resonant Success at TeV Scale: The study establishes that the observed baryon asymmetry can be generated without resonant enhancement. The mechanism relies on the specific interplay between flavoured CP asymmetries and hierarchical washouts rather than mass degeneracy.
Flavor-Dependent Dynamics: The analysis highlights that the final baryon asymmetry is determined by the survival of lepton asymmetry in a specific flavor direction where the washout is weak, while asymmetries in other directions are strongly washed out. This "hierarchical washout" is crucial for the success of the model.
Parameter Space Identification: The work identifies viable regions in the parameter space compatible with all theoretical and experimental constraints, specifically linking successful baryogenesis to relatively small heavy neutrino mass splittings ( $\Delta M$ ) that remain well within the non-resonant regime ( $\Delta M \gg \Gamma$ ).

Results

Baryon Asymmetry: The numerical analysis successfully reproduces the observed baryon asymmetry ( $\eta_B \approx 6.12 \times 10^{-10}$ ) for heavy neutrino masses between 10 TeV and 100 TeV.
Washout Hierarchy: For successful benchmark points, the washout factor $K_{1\alpha}$ is found to be weak ( $<1$ ) in one flavor direction (e.g., $\tau$ ) while being strong ( $\gg 1$ ) in the others. The surviving asymmetry in the weakly washed-out channel dominates the final result.
Mass Splitting Correlation: Points yielding the correct baryon asymmetry are predominantly clustered in regions of small mass splitting ( $\Delta M = M_2 - M_1$ ). However, the authors confirm that for all viable points, the condition for resonant leptogenesis ( $|M_2 - M_1| \lesssim \Gamma_{N_1, N_2}$ ) is strictly violated, confirming the non-resonant nature of the solution.
Benchmark Points: Three benchmark points (BP1, BP2, BP3) are presented with heavy neutrino masses ranging from $\sim 16$ TeV to $\sim 97$ TeV. In all cases, the model satisfies the $\mu \to e\gamma$ constraint by many orders of magnitude and reproduces the observed $Y_B$ through the cancellation and summation of individual flavor asymmetries.

Significance
The paper claims that the distinct Yukawa structure of the Aligned Two-Higgs Doublet Model, combined with the dynamics of fully flavoured leptogenesis, provides a viable mechanism for generating the universe's baryon asymmetry at the TeV scale without invoking resonant enhancement. The work underscores the essential role of flavor-dependent washouts and the complex alignment parameter in realizing the observed lepton asymmetry. It offers a unified framework that simultaneously addresses the origin of active neutrino masses, charged lepton flavor violation constraints, and baryogenesis, demonstrating that successful baryogenesis is achievable in a non-resonant regime through the specific interplay of multiple Higgs doublets and heavy neutrino flavors.

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