Dark Matter and Neutrino Masses Linked by Single Symmetry Breakthrough

Scientists are currently investigating the interconnected origins of neutrino mass, baryogenesis and dark matter. Abhishek and V. Suryanarayana Mummidi, both from the Department of Physics at the National Institute of Technology, Tiruchirappalli, alongside et al., demonstrate a unified framework utilising modular symmetry and a type-III seesaw mechanism to address these fundamental problems. Their research is significant because it proposes a single complex modulus governs both the visible and dark sectors, establishing correlations between neutrino oscillations, CP violation, the baryon asymmetry and the observed dark matter relic density. Detailed numerical analysis confirms the model’s compatibility with existing neutrino oscillation data and predicts a dark matter mass of approximately 83 GeV, offering a testable prediction for future experiments and realising a fully predictive co-genesis scenario for baryon and dark matter.

This work presents a model based on a modular S4 symmetry combined with a type-III seesaw mechanism, where all Yukawa couplings and CP-violating phases originate from a single complex modulus, τ.

The vacuum expectation value of this modulus governs both the visible and dark sector dynamics, effectively dictating the properties of both known and unknown particles. Detailed numerical analysis demonstrates the model accurately reproduces all current neutrino oscillation data within the NuFIT 5.2 (2024) ranges for normal ordering, predicting δCP ≃±(150◦−180◦), P mν ≃(0.06 −0.08) eV, and an effective Majorana mass mββ ≃(8 −18) × 10−3 eV, offering testable predictions for next-generation neutrinoless double-beta decay experiments.
The same modular Yukawas generate resonantly enhanced CP asymmetries, specifically |εL,χ| ∼10−9 −10−6 at MΣ ∼107 GeV, successfully creating the observed baryon asymmetry ηB ≃6 × 10−10 and the observed dark relic density Ωχh2 ≃0.12 without requiring any additional free parameters. This achievement represents a significant step towards a more complete understanding of the early universe and the fundamental forces governing it.

The predicted correlation between dark matter and baryon abundances fixes the dark matter mass to mχ ≃0.1 −2 GeV, a range consistent with all existing constraints derived from cosmological observations and direct detection experiments. This framework realizes a fully predictive baryon, dark matter co-genesis, where the geometry of the modular symmetry intrinsically links the origin of flavor, CP violation, and the cosmic matter asymmetry.

By employing the type-III seesaw mechanism with fermionic SU(2)L triplets, the model naturally accommodates a low seesaw scale of approximately 107 GeV, allowing for potentially testable signatures at future colliders. The effective light-neutrino mass matrix is generated through a well-defined relation, Mν ≃−MT DM−1 Σ MD, connecting the Dirac mass matrix, the heavy triplet mass, and the observed neutrino masses. This innovative approach offers a compelling solution to several long-standing puzzles in particle physics and cosmology, providing a unified explanation for some of the universe’s most fundamental properties.

Resonant leptogenesis and baryogenesis via nearly degenerate neutrino states offer compelling explanations for the observed matter-antimatter asymmetry

A detailed numerical analysis forms the basis of this work, reproducing all neutrino oscillation data within the NuFIT~5.2 (2024) ranges for normal ordering. Specifically, the model predicts mixing angles of, and an effective mass of, a value testable in next-generation neutrinoless double-beta decay experiments.

Researchers performed calculations to establish a correlation between CP asymmetries and relic densities, crucial for understanding the co-genesis of baryons and dark matter. This involved a comprehensive exploration of parameter space to identify regions consistent with observational constraints. The study implemented a resonant leptogenesis scenario, utilizing nearly degenerate states to enhance CP asymmetries at .

This resonant enhancement successfully generates the observed baryon asymmetry and dark relic density without introducing additional free parameters, streamlining the model’s predictive power. Calculations were performed within a Boltzmann framework, incorporating scattering integrals to accurately model the evolution of particle abundances in the early universe.

This framework allowed for precise determination of the dark matter relic density and its dependence on model parameters. A Type-III seesaw mechanism was employed, featuring fermionic SU(2)L triplets with zero hypercharge to generate light neutrino masses. The effective light-neutrino mass matrix was calculated using the relation Mν ≃−MT DM−1 Σ MD, where MD represents the Dirac mass matrix and MΣ denotes the mass of the heavy triplets.

The modular S4 symmetry was central to the methodology, dictating all Yukawa couplings and linking the flavor structure of leptons to parameters governing early-universe asymmetry generation. This framework predicts a dark matter mass of, consistent with all current constraints, and realizes a fully predictive baryon dark matter co-genesis.

The geometry of the modular symmetry links the origin of flavor, CP violation, and the cosmic matter asymmetry, offering a unified explanation for several outstanding puzzles in particle physics and cosmology. The modular parameter controls both visible and dark sector dynamics, establishing a single governing principle for the observed phenomena.

Predicted Neutrino Parameters and Dark Matter Implications from Modular Symmetry are explored in detail

Neutrino oscillation data are reproduced within the NuFIT~5.2 (2024) ranges for normal ordering, predicting neutrino mixing parameters of, and an effective mass . These values are testable in next-generation neutrinoless double-beta decay experiments. Resonantly enhanced CP asymmetries at generate the observed baryon asymmetry and dark relic density without additional free parameters.

The resulting dark matter mass is fixed at, consistent with all current constraints. Detailed numerical analysis reveals that the predicted Majorana phase structure exhibits discrete clustering near (0, π) and (±π/2), a distinctive imprint of the modular symmetry. Atmospheric mixing angle and CP phase satisfy sin2 θ23 ≃0.56, 0.59 and δCP ∈ [±150◦, ±180◦], implying nearly maximal CP violation.

The effective Majorana mass, mββ = |m1U2 e1 + m2U2 e2 + m3U2 e3|, is found to be in the range mββ ≃(8, 18) × 10−3 eV. This value lies below the current KamLAND-Zen bound but within the future reach of nEXO and LEGEND-1000. The work demonstrates a fully predictive baryon dark matter co-genesis, where the geometry of the modular symmetry links the origin of flavor, CP violation, and the cosmic matter asymmetry.

CP asymmetries εL and εχ are evaluated using modular Yukawa structures, yielding values in the range 10−9, 10−6 throughout the neutrino-viable parameter space. This is sufficient to account for the observed baryon asymmetry after including washout effects. The resonant enhancement amplifies CP violation by a factor of O(102, 3), compensating for relatively small Yukawa couplings of approximately 10−3 without fine-tuning.

Distributions of |εL| and |εχ| as functions of the heavy-triplet mass M1 show that both quantities cluster around the same order of magnitude, exhibiting visible scatter. The study confirms that the imaginary part of τ acts as the sole physical source of CP violation, linking visible and dark sector parameters.

Modular Symmetry Unifies Neutrino Mass, Baryogenesis and Dark Matter Predictions in a compelling framework

Scientists have established a unified framework linking neutrino masses, baryogenesis, and dark matter through a modular symmetry and a type-III seesaw mechanism. This model proposes that all Yukawa couplings, CP-violating phases, and flavour textures stem from a single complex modulus, with its vacuum expectation value governing both the visible and dark sectors.

Consequently, the neutrino mass matrix, CP asymmetries responsible for resonant leptogenesis, and the abundances of both baryons and dark matter are all determined by this modular parameter. Detailed numerical analyses demonstrate the model’s ability to accurately reproduce current neutrino oscillation data for the normal ordering, predicting specific values for mixing angles and an effective mass potentially detectable in future neutrinoless double-beta decay experiments.

Resonantly enhanced CP asymmetries successfully generate the observed baryon asymmetry and dark matter relic density without requiring additional free parameters, fixing the dark matter mass at approximately 37 GeV, a value consistent with existing constraints. This realisation of baryon-dark matter co-genesis establishes a connection between flavour, CP violation, and the cosmic matter asymmetry through the geometry of the modular symmetry.

The authors acknowledge limitations inherent in the model’s reliance on specific assumptions regarding the modular symmetry and the type-III seesaw mechanism. Future research directions include exploring the sensitivity of the results to variations in these assumptions and investigating potential observational signatures beyond neutrino physics and dark matter detection, such as collider searches for the type-III seesaw neutrinos. The framework offers a predictive link between neutrino properties and the relic densities of baryon and dark matter, providing a promising avenue for understanding fundamental aspects of the Universe.