[Paper Review] Fermion masses and mixings in SO(10) models and the neutrino challenge to SUSY GUTs

Stefano Bertolini, Michal Malinský+1 more|arXiv (Cornell University)|May 1, 2006

Particle physics theoretical and experimental studies45 citations

TL;DR

This paper investigates fermion masses and mixings in SO(10) grand unified theories with one 10_H and one ¯126_H Higgs, analyzing the interplay of type-I and type-II seesaw mechanisms for neutrino masses. It finds that the minimal supersymmetric SO(10) GUT with renormalizable Higgs sector fails to reproduce fermion data consistently, strongly suggesting a non-SUSY scenario for gauge unification.

ABSTRACT

We present a detailed study of the quark and lepton mass spectra in a SO(10) framework with one 10_H and one \bar{126}_H Higgs representations in the Yukawa sector. We consider in full generality the interplay between type-I and type-II seesaws for neutrino masses. We first perform a \chi^2 fit of fermion masses independent on the detailed structure of the GUT Higgs potential and determine the regions in the parameter space that are preferred by the fermion mass sum rules. We then apply our study to the case of the minimal renormalizable SUSY SO(10) GUT with one 10_H, one \bar{126}_H, one 126_H, and one 210_H Higgs representations. By requiring that proton decay bounds are fulfilled we identify a very limited area in the parameter space where all fermion data are consistently reproduced. We find that in all cases gauge coupling unification in the supersymmetric scenario is severely affected by the presence of lighter than GUT (albeit B-L conserving) states. We then conclusively show that the minimal supersymmetric SO(10) scenario here considered is not consistent with data. The fit of neutrino masses with type-I and type-II seesaws within a renormalizable SO(10) framework strongly suggests a non-SUSY scenario for gauge unification.

Motivation & Objective

• To analyze the interplay between type-I and type-II seesaw mechanisms in SO(10) models for neutrino mass generation.
• To perform a χ^2 fit of quark and lepton masses independent of the GUT Higgs potential structure.
• To test the consistency of the minimal renormalizable SUSY SO(10) GUT with one 10_H, one ¯126_H, one 126_H, and one 210_H Higgs representations against fermion data and proton decay bounds.
• To assess the impact of lighter-than-GUT B-L conserving states on gauge coupling unification in the SUSY scenario.
• To determine whether the minimal SUSY SO(10) framework can consistently reproduce all fermion mass and mixing data.

Proposed method

• A χ^2 fitting procedure is applied to fermion masses and mixings using the full parameter space of the SO(10) model with 10_H and ¯126_H Higgs representations.
• The analysis includes both type-I and type-II seesaw contributions to neutrino masses, treating them on equal footing without assuming dominance of one over the other.
• The model is extended to the minimal renormalizable SUSY SO(10) GUT with four Higgs representations: 10_H, ¯126_H, 126_H, and 210_H.
• Proton decay bounds are imposed as a stringent constraint on the parameter space, particularly affecting the 126_H and 210_H contributions.
• Gauge coupling unification is evaluated numerically, considering the presence of lighter-than-GUT states that break B-L symmetry only via Higgs mixing.
• The consistency of the model is tested by comparing predicted fermion masses and mixings with experimental data across all generations.

Experimental results

Research questions

• RQ1 Can the minimal renormalizable SUSY SO(10) GUT with 10_H, ¯126_H, 126_H, and 210_H Higgs representations simultaneously reproduce all fermion masses and mixings?
• RQ2 What is the allowed parameter space when proton decay bounds are applied in this SUSY SO(10) framework?
• RQ3 How do type-I and type-II seesaw mechanisms jointly affect neutrino mass predictions in a renormalizable SO(10) model?
• RQ4 To what extent do lighter-than-GUT B-L conserving states disrupt gauge coupling unification in the SUSY scenario?
• RQ5 Does the observed fermion mass spectrum in SO(10) models with both seesaw mechanisms point toward a non-SUSY completion of the GUT?

Key findings

• The minimal renormalizable SUSY SO(10) GUT with the specified Higgs content fails to reproduce all fermion data consistently, even after imposing proton decay bounds.
• A very limited region of the parameter space satisfies all constraints, and this region is incompatible with successful gauge coupling unification.
• The presence of lighter-than-GUT states, even if B-L conserving, severely disrupts gauge coupling unification in the SUSY scenario.
• The interplay of type-I and type-II seesaws in a renormalizable SO(10) model leads to a strong preference for a non-SUSY completion of the GUT.
• The study concludes that the minimal SUSY SO(10) model is inconsistent with current fermion data and proton decay limits.
• The results strongly suggest that gauge unification in SO(10) may require a non-SUSY framework to remain viable.