Resonant Type-II + Type-I Hybrid Leptogenesis in SO(10) with Triplet--Neutrino Mass Degeneracy $M_T \simeq M_{N_3}$

TL;DR

The paper introduces a novel hybrid leptogenesis mechanism in renormalizable SO(10) that arises when the scalar triplet mass $M_T$ is quasi-degenerate with the heaviest RH neutrino $M_3$, forcing interference between type-I and type-II decay channels. This interference generates a CP-violating invariant $\phi_{\rm HR} = \arg(\mu f Y_\nu^\dagger)$ that cannot be removed by field redefinitions, producing a resonant enhancement of the baryon asymmetry without requiring extreme Yukawa hierarchies. Numerical solutions of flavour-covariant Boltzmann equations show that the observed $Y_B \simeq 8.7\times10^{-11}$ is naturally obtained for heavy scales around $10^{11}$ GeV, with moderate washout and $\mathcal{O}(1)$ phases, and the model makes testable predictions for lepton-flavour violation and leptonic electric dipole moments. The framework also implies indirect collider signatures through CP-odd Higgs observables and other dimension-six operators, linking high-scale baryogenesis to measurable low-energy CP violation and LFV phenomena. Overall, the work provides a predictive, falsifiable connection between SO(10) unification, neutrino masses, and CP violation across energy scales, offering multiple avenues for experimental validation in near-future experiments.

Abstract

The origin of the baryon asymmetry of the Universe remains one of the central open problems in particle physics and cosmology. We identify a new regime of \emph{hybrid resonant leptogenesis} in renormalizable SO(10) grand unified theories, where a quasi-degeneracy between the scalar triplet and the heaviest right-handed neutrino, \( M_T \simeq M_{N_3}, \) induces an unavoidable interference between type-I and type-II decay amplitudes. This interference gives rise to a physical CP-violating phase, \( φ_{\rm HR} = \arg(μf Y_ν^\dagger), \) which cannot be removed by field redefinitions and leads to a resonant enhancement of the baryon asymmetry without extreme Yukawa hierarchies or tuning. We show that the observed asymmetry, \( Y_B \simeq 8.7 \times 10^{-11}, \) is naturally reproduced for masses around \(10^{11}\,\mathrm{GeV}\), moderate washout, and \(\mathcal{O}(1)\) phases. The mechanism is predictive and testable, with correlated implications for lepton-flavour violation and electric dipole moments.

Figures (9)

• Figure 1: Resonant enhancement of the hybrid CP asymmetry $\varepsilon^{\rm tot}_3$ as a function of the degeneracy parameter $\delta = (M_T - M_3)/M_3$. The maximum occurs for $|\delta| \sim \Gamma_3/M_3$, where the interference between type-I and type-II contributions becomes resonant.
• Figure 2: Representative numerical solution of the flavour-covariant Boltzmann equations showing the evolution of the $N_3$ abundance, the scalar triplet abundance, and the lepton asymmetry as functions of $z = M_T/T$.
• Figure 3: Comparison of different LHC-sensitive observables induced by the hybrid leptogenesis sector as a function of the effective heavy scale $\Lambda \sim M_T$. The solid, dashed, dash--dotted, and dotted curves correspond respectively to CP-odd effects in $h\to\tau^+\tau^-$, deviations in $h\to\mu^+\mu^-$, lepton-flavour-violating dilepton production, and electroweak precision observables. The horizontal dashed line indicates the projected sensitivity of HL-LHC measurements.
• Figure 4: Evolution of the normalized hybrid CP-odd observable $\mathcal{A}_{\rm CP}/\mathcal{A}_{\rm CP}^{\rm max}$ as a function of the dimensionless variable $z = M_T/T$ for representative values of the effective washout parameter $K_{\rm eff}$. Smaller $K_{\rm eff}$ corresponds to weak washout and leads to a rapid saturation of the CP asymmetry, while stronger washout delays the freeze-out of the asymmetry.
• Figure 5: Hybrid resonant leptogenesis in the plane of the hybrid CP phase $\phi_{\rm HR}$ and the heavy scale $\Lambda \sim M_T \sim M_{N_3}$. Left panel: colour shading shows a proxy for the baryon asymmetry $Y_B$ generated through the resonant interference of type-I and type-II contributions; the horizontal band indicates the region compatible with the observed baryon asymmetry. Right panel: indirect collider sensitivity to the same hybrid CP phase through CP-odd Higgs observables, illustrating the link between high-scale baryogenesis and precision measurements at the LHC.