The type-I seesaw framework can explain light-neutrino masses and generate a lepton asymmetry through out-of-equilibrium decays of heavy right-handed neutrinos, which sphaleron processes convert into a baryon asymmetry. Its conventional version, however, places the right-handed neutrinos at scales that are difficult to access experimentally. With order-one Yukawa couplings, neutrino masses around 10^13 GeV can arise naturally, while hierarchical masses above roughly 10^9 GeV are generally needed to produce enough asymmetry. Alternative low-scale approaches include resonant leptogenesis and leptogenesis via neutrino oscillations, but both typically require a highly degenerate right-handed-neutrino spectrum.

The study instead considers a scalar singlet S that couples to different right-handed neutrinos through terms of the form SN_IN_J. These interactions open the decay channel N_I → N_JS and add one-loop vertex and self-energy contributions to the CP asymmetries in neutrino decays. The analysis treats this as a theoretical possibility, not an experimentally established mechanism, and finds that the scalar-assisted process can produce a sufficient asymmetry at TeV scales without mass degeneracy.

Yan Shao and Zhen-hua Zhao identify flavons in flavor-symmetry neutrino models as natural candidates for S. These scalar fields commonly acquire nonzero vacuum expectation values that help generate right-handed-neutrino masses. The authors first illustrate the idea with the classic A₄ flavor-symmetry model. That A₄ model predicts tri-bimaximal neutrino mixing, including a vanishing mixing angle θ₁₃, a prediction ruled out by experimental measurements.

For their numerical analysis, the authors therefore use a different flavor-symmetry construction based on A₄ and three auxiliary Z₂ symmetries. It is designed to realize the trimaximal TM1 mixing pattern, which modifies the tri-bimaximal pattern in the two-three plane and is consistent with current experimental results. The model contains one relevant flavon, S, which is allowed by the flavor symmetries to couple only to the second and third right-handed neutrinos through α₀SN₂⁰N₃⁰. Its vacuum expectation value generates an off-diagonal right-handed-neutrino mass term and the rotation required to transform tri-bimaximal mixing into TM1 mixing.

The same flavon interaction also supplies the couplings used in the leptogenesis calculation, making the mixing structure and baryogenesis mechanism consequences of one flavor-symmetry term rather than independent additions. The authors assume that the decoupled N₁ is the heaviest right-handed neutrino and neglect its effects on leptogenesis, while taking M₃ > M₂. Their flavor-dependent Boltzmann equations include standard neutrino decays and inverse decays, the transition N₃ → N₂S, and dominant scalar-mediated ΔL = 2 scattering processes. The resulting baryon-to-entropy ratio is compared with the observed value, (8.69 ± 0.04) × 10⁻¹¹.

In a representative numerical example, M₂ is 2 TeV, M₃ is 4 TeV, and both the flavon mass and the Higgs–flavon trilinear coupling β are 1 GeV. With |α₀| = 0.1, conventional flavored CP asymmetries from N₃ decays are estimated at about 10⁻¹⁶–10⁻¹⁴, whereas the flavon-mediated vertex and self-energy contributions raise the total to approximately 10⁻⁷–10⁻⁵. The new decay channel must be kinematically open, requiring m_S < M₃ − M₂. When it closes, the additional contributions and the D₃₂ transition disappear, and the conventional asymmetries are too small to account for the observed value in the TeV-scale regime examined.

Parameter scans reproduce the observed baryon asymmetry in significant regions for both normal and inverted light-neutrino mass orderings. In the normal-ordering case, the authors find successful leptogenesis with M₂ as low as about 200 GeV under their parameter setup, with viable β values extending to roughly 10 GeV. As M₂ increases, larger β values become viable; at M₂ = 5 TeV, successful regions occur at β values of order 10 TeV. The inverted-ordering case exhibits similar qualitative behavior but has a more restricted viable parameter space. Changing the flavon mass has only a slight effect on the final asymmetry in the studied scans.

The viable regions also satisfy constraints from the Higgs and flavon scalar sector. Higgs signal-strength data limit the scalar mixing angle to |sin θ| ≲ 0.3, and the Higgs invisible branching ratio is constrained to 0.23 or less. The scalar potential must also remain stable at its vacuum and perturbative. These requirements remove some parameter space but leave viable regions in both mass orderings. The study is theoretical and model-specific: its numerical conclusions apply to the selected TM1 flavor-symmetry construction and parameter ranges, rather than establishing a unique explanation for the cosmic asymmetry.

Subject of Research: Theoretical modeling of flavon-assisted low-scale leptogenesis in flavor-symmetry neutrino models

Article Title: Flavon assisted low scale leptogenesis

Article References: Shao, Y., & Zhao, Z.-H. (2026). Flavon assisted low scale leptogenesis. The European Physical Journal C, 86(10), Article 1179. https://doi.org/10.1140/epjc/s10052-026-16421-5

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16421-5

Keywords: leptogenesis, flavons, right-handed neutrinos, baryon asymmetry, TM1 mixing, type-I seesaw, CP violation, Higgs portal, neutrino flavor symmetry, Flavon, assisted, scale