Dirac-Phase CP-Violation in the Low-Scale Type-I Seesaw with Three Right-Handed Neutrinos
Abstract
We study the low-scale type-I seesaw with three right-handed neutrinos (i.e. heavy Majorana neutrinos) when the CP-violation arises solely from the low-energy Dirac phase δ of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix and the heavy neutrinos have testable mixings. We derive a CP-conserving and non-real structure of the 3× 3 orthogonal matrix entering the Casas-Ibarra parametrisation in terms of two real angles and one single imaginary parameter, ensuring that the only CP-violating phases in the neutrino Yukawa couplings are those of the PMNS matrix. We then focus on the case of CP-violation from δ alone and discuss the phenomenological implications of this hypothesis. We concentrate on quasi-degenerate heavy Majorana neutrinos with masses within ∼ (0.1−100) GeV, as relevant for low-scale leptogenesis. Only certain subregions of the full ternary space defined by the ratios Θ2e:Θ2μ:Θ2τ - where Θ2α denotes the squared coupling of the heavy neutrinos to leptons of flavour α= e, μ, τ - are compatible with Dirac-phase CP-violation while being testable at collider experiments. Our assumption also implies specific forms of the effective Majorana mass parameter that can be tested at neutrinoless double-beta decay searches. Finally, low-scale leptogenesis under this restriction can reproduce the baryon asymmetry of the Universe (BAU) and be tested through the combination of direct heavy neutral lepton searches and neutrino experiments. The BAU vanishes in the exact limit of CP-conserving values of the Dirac phase δ= 0, π, 2π, but the observed BAU can be reproduced within the testable region even if δ deviates from these values by a factor as small as 𝒪(10−5), with important implications for ultraviolet completions with approximate CP-symmetry.
Related
- On the Maximal CP Violation in Leptogenesis with Two Right Handed Neutrinos
- Massive right-handed neutrinos in B̅ → D* τX̅ decay
- Leptogenesis without on-shell right-handed neutrinos
- Leptogenesis without on-shell right-handed neutrinos
- Non-resonant Flavoured leptogenesis with aligned two-Higgs doublet model and right-handed neutrinos
BibTeX
@misc{granelli2026diracphase,
title = {{Dirac-Phase CP-Violation in the Low-Scale Type-I Seesaw with Three Right-Handed Neutrinos}},
author = {Alessandro Granelli and Juraj Klarić and S. T. Petcov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.31454},
eprint = {2605.31454},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.31454},
}
RIS
TY - UNPB
TI - Dirac-Phase CP-Violation in the Low-Scale Type-I Seesaw with Three Right-Handed Neutrinos
AU - Alessandro Granelli
AU - Juraj Klarić
AU - S. T. Petcov
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2605.31454
UR - https://arxiv.org/abs/2605.31454
AB - We study the low-scale type-I seesaw with three right-handed neutrinos (i.e. heavy Majorana neutrinos) when the CP-violation arises solely from the low-energy Dirac phase δ of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix and the heavy neutrinos have testable mixings. We derive a CP-conserving and non-real structure of the 3× 3 orthogonal matrix entering the Casas-Ibarra parametrisation in terms of two real angles and one single imaginary parameter, ensuring that the only CP-violating phases in the neutrino Yukawa couplings are those of the PMNS matrix. We then focus on the case of CP-violation from δ alone and discuss the phenomenological implications of this hypothesis. We concentrate on quasi-degenerate heavy Majorana neutrinos with masses within ∼ (0.1−100) GeV, as relevant for low-scale leptogenesis. Only certain subregions of the full ternary space defined by the ratios Θ^2_e:Θ^2_μ:Θ^2_τ - where Θ^2_α denotes the squared coupling of the heavy neutrinos to leptons of flavour α= e, μ, τ - are compatible with Dirac-phase CP-violation while being testable at collider experiments. Our assumption also implies specific forms of the effective Majorana mass parameter that can be tested at neutrinoless double-beta decay searches. Finally, low-scale leptogenesis under this restriction can reproduce the baryon asymmetry of the Universe (BAU) and be tested through the combination of direct heavy neutral lepton searches and neutrino experiments. The BAU vanishes in the exact limit of CP-conserving values of the Dirac phase δ= 0, π, 2π, but the observed BAU can be reproduced within the testable region even if δ deviates from these values by a factor as small as 𝒪(10^−5), with important implications for ultraviolet completions with approximate CP-symmetry.
ER -