Reality-constrained minimal Yukawa structure in SO(10) GUT
- 1Jožef Stefan Institute
- 2Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati
Abstract
A bstract : We investigate the minimal Yukawa sector of grand unified theories based on SO(10) symmetry, consisting of a Higgs structure with representations 10 ℝ ⊕ 120 ℝ ⊕ 126 . Taking 10 ℝ and 120 ℝ to be real scalars, we derive the associated SO(10) reality conditions for their weak-doublet constituents and revisit previously reported fermion mass relations. Our analysis revises earlier results by introducing a relative sign difference between the reality constraints on the two weak doublets in 120 ℝ , yielding a new parameter (a magnitude) in the fermion mass relations. We establish this result through four complementary derivations: an explicit SO(10) tensorial calculation of invariants, an analytic reformulation via the Pati-Salam embedding, an algorithm for transporting reality structures from parent to daughter irreps, and an SU(5)-based calculation using the SO(10) oscillator method, all giving consistent results. The methods for determining reality conditions can be applied to any parent-daughter representation pair of SO(10) and its Pati-Salam subgroup, while the transport algorithm generalizes to arbitrary groups H ⊂ G . Incorporating the correct mass relations, we perform an extensive numerical scan and find that the model successfully reproduces SM fermion masses and mixings, including recent precision measurements of solar oscillation parameters by JUNO. It accommodates both octants of θ ₂₃ while mildly disfavoring δ PMNS ∼ (140 ° , 220 ° ). The model predicts a strongly hierarchical right-handed neutrino spectrum (10 ⁵ , 10 ¹² , 10 ¹⁵ ) GeV and a neutrinoless double beta decay parameter m ββ ∼ 3-4 meV, just below future experimental sensitivity. Proton decay is dominated by p→ π+ν̅ p → π + ν ¯ and p → π ⁰ e ⁺ , making these channels testable in upcoming experiments.
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BibTeX
@article{saad2026realityconstrained,
title = {{Reality-constrained minimal Yukawa structure in SO(10) GUT}},
author = {Shaikh Saad and Vasja Susič},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)036},
url = {https://link.springer.com/10.1007/JHEP10(2026)036},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Reality-constrained minimal Yukawa structure in SO(10) GUT
AU - Shaikh Saad
AU - Vasja Susič
PY - 2026
DA - 2026/10/02
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)036
UR - https://link.springer.com/10.1007/JHEP10(2026)036
AB - A bstract : We investigate the minimal Yukawa sector of grand unified theories based on SO(10) symmetry, consisting of a Higgs structure with representations 10 ℝ ⊕ 120 ℝ ⊕ 126 . Taking 10 ℝ and 120 ℝ to be real scalars, we derive the associated SO(10) reality conditions for their weak-doublet constituents and revisit previously reported fermion mass relations. Our analysis revises earlier results by introducing a relative sign difference between the reality constraints on the two weak doublets in 120 ℝ , yielding a new parameter (a magnitude) in the fermion mass relations. We establish this result through four complementary derivations: an explicit SO(10) tensorial calculation of invariants, an analytic reformulation via the Pati-Salam embedding, an algorithm for transporting reality structures from parent to daughter irreps, and an SU(5)-based calculation using the SO(10) oscillator method, all giving consistent results. The methods for determining reality conditions can be applied to any parent-daughter representation pair of SO(10) and its Pati-Salam subgroup, while the transport algorithm generalizes to arbitrary groups H ⊂ G . Incorporating the correct mass relations, we perform an extensive numerical scan and find that the model successfully reproduces SM fermion masses and mixings, including recent precision measurements of solar oscillation parameters by JUNO. It accommodates both octants of θ ₂₃ while mildly disfavoring δ PMNS ∼ (140 ° , 220 ° ). The model predicts a strongly hierarchical right-handed neutrino spectrum (10 ⁵ , 10 ¹² , 10 ¹⁵ ) GeV and a neutrinoless double beta decay parameter m ββ ∼ 3-4 meV, just below future experimental sensitivity. Proton decay is dominated by p→ π^+ν̅ p → π + ν ¯ and p → π ⁰ e ⁺ , making these channels testable in upcoming experiments.
SN - 1029-8479
ER -