[Paper Review] A realistic pattern of fermion masses from a five-dimensional SO(10) model

Ferruccio Feruglio, Ketan M. Patel+1 more|arXiv (Cornell University)|Jul 2, 2015

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents a five-dimensional supersymmetric SO(10) grand unified model with anarchic Yukawa couplings on an $S^1/(\mathbb{Z}_2 \times \mathbb{Z}_2')$ orbifold, where fermion mass hierarchies arise from exponential wave function profiles due to bulk masses. The model successfully reproduces the observed fermion masses and mixing angles, predicts a normal neutrino mass ordering with $m_1 < 0.01$ eV, and favors a hierarchical right-handed neutrino spectrum incompatible with thermal leptogenesis.

ABSTRACT

We provide a unified description of fermion masses and mixing angles in the framework of a supersymmetric grand unified SO(10) model with anarchic Yukawa couplings of order unity. The space-time is five dimensional and the extra flat spatial dimension is compactified on the orbifold $S^1/(Z_2 \ imes Z_2')$, leading to Pati-Salam gauge symmetry on the boundary where Yukawa interactions are localised. The gauge symmetry breaking is completed by means of a rather economic scalar sector, avoiding the doublet-triplet splitting problem. The matter fields live in the bulk and their massless modes get exponential profiles, which naturally explain the mass hierarchy of the different fermion generations. Quarks and leptons properties are naturally reproduced by a mechanism, first proposed by Kitano and Li, that lifts the SO(10) degeneracy of bulk masses in terms of a single parameter. The model provides a realistic pattern of fermion masses and mixing angles for large values of $\ an\\beta$. It favours normally ordered neutrino mass spectrum with the lightest neutrino mass below 0.01 eV and no preference for leptonic CP violating phases. The right handed neutrino mass spectrum is very hierarchical and does not allow for thermal leptogenesis. We analyse several variants of the basic framework and find that the results concerning the fermion spectrum are remarkably stable.

Motivation & Objective

• To address the fermion mass hierarchy and flavor structure in SO(10) grand unified theories using a higher-dimensional framework.
• To resolve the doublet-triplet splitting problem through gauge symmetry breaking via orbifold compactification.
• To naturally explain the observed mass hierarchies and mixing patterns of quarks and leptons using a single parameter controlling bulk masses.
• To test the viability of the model in reproducing low-energy fermion observables, including neutrino masses and mixing angles.
• To assess the implications for leptogenesis and the right-handed neutrino mass spectrum.

Proposed method

• Compactification of five-dimensional spacetime on the orbifold $S^1/(\mathbb{Z}_2 \times \mathbb{Z}_2')$ to break SO(10) to Pati-Salam gauge symmetry on the fixed branes.
• Localizing Yukawa interactions on the branes while matter fields propagate in the bulk, leading to exponentially localized zero-mode wave functions.
• Introducing bulk masses for matter fields that generate hierarchical wave function profiles, explaining the fermion mass hierarchy via a single parameter.
• Implementing spontaneous SO(10) breaking to SU(5)×U(1)_X via a bulk scalar multiplet to distinguish quark and lepton sectors.
• Using the Kitano-Li mechanism to lift degeneracy in bulk masses and generate realistic Yukawa textures.
• Solving the 5D Kaluza-Klein zero-mode equations to derive profile matrices in terms of the Cabibbo angle $\lambda$, which are then matched to observed fermion masses and mixings.

Experimental results

Research questions

• RQ1 Can a 5D SO(10) GUT with anarchic Yukawa couplings reproduce the observed fermion mass hierarchies and mixing angles?
• RQ2 How does wave function localization from bulk masses in a compactified extra dimension explain the hierarchical structure of fermion masses?
• RQ3 What is the impact of the orbifold compactification on gauge symmetry breaking and the resolution of the doublet-triplet splitting problem?
• RQ4 Does the model predict a viable neutrino mass spectrum, and what are the implications for leptogenesis?
• RQ5 How stable are the fermion mass predictions under variations of the model's parameters and structure?

Key findings

• The model successfully reproduces the observed pattern of fermion masses and mixing angles for large $\tan\beta$ values.
• The neutrino mass spectrum is predicted to be normally ordered with the lightest neutrino mass below 0.01 eV.
• The model shows no preference for large leptonic CP-violating phases, consistent with current experimental constraints.
• The right-handed neutrino mass spectrum is highly hierarchical, disfavoring thermal leptogenesis due to insufficient reheating temperature.
• Yukawa matrices for quarks and leptons are derived with specific complex phases and hierarchical structures, matching the Cabibbo angle expansion.
• The results are remarkably stable across multiple variants of the model, indicating robustness of the fermion spectrum prediction.