Hybrid Type-I and Type-II Leptogenesis in Minimal Renormalizable $\mathrm{SO}(10)$

Abstract

We investigate flavoured hybrid leptogenesis in a minimal renormalizable $\mathrm{SO}(10)$ framework in which both Type-I and Type-II seesaw interactions contribute to the generation of the cosmological baryon asymmetry. We consider a regime where heavy Majorana neutrinos and electroweak scalar triplets are independently quasi-degenerate, leading to resonant enhancement in each sector, while additional CP-violating contributions arise from loop-induced interference between fermionic and scalar interactions. These hybrid contributions vanish if either sector is absent, providing a genuinely new source of CP violation beyond conventional single-sector leptogenesis. The evolution of the lepton asymmetry is studied using a flavour-covariant density-matrix formalism that consistently incorporates flavour coherence, spectator effects, and washout processes. We show that the observed baryon asymmetry, $Y_B\simeq8.7\times10^{-11}$, can be reproduced for representative parameter regions with heavy mass scales of $10^{10}$--$10^{12},\mathrm{GeV}$ and perturbative Yukawa couplings. To characterize the flavour structure of the hybrid interference terms, we introduce the scalar quantity [ J_{\rm hybrid}={\rm Im}!\left[\mu,{\rm Tr}!\left(fY_\nu^\dagger Y_\nu\right)\right], ] which provides a compact parametrization of the flavour contractions entering the hybrid amplitudes in the flavour basis adopted here. We emphasize that it serves as a convenient diagnostic of the hybrid interference terms rather than a complete basis-independent measure of CP violation. The same interactions responsible for baryogenesis can also induce charged-lepton flavour violation and electric dipole moments, linking neutrino mass generation, grand unification, and future precision searches for CP violation.