[Paper Review] Msgut Reborn

Charanjit S. Aulakh|arXiv (Cornell University)|Jul 23, 2006

Particle physics theoretical and experimental studies8 citations

TL;DR

This paper proposes a supersymmetric SO(10) GUT model using a 10-120-126 Higgs system to simultaneously fit charged fermion masses and generate viable Type I seesaw neutrino masses. By introducing small 126-plet couplings, it achieves accurate fits (χ² < 0.2) and naturally enhances neutrino masses by 10²–10³ times compared to the 10-126 scenario, resolving a key challenge in next-to-minimal SUSY GUTs while requiring CP violation for full lepton mixing consistency.

ABSTRACT

We present examples of fits of fermion mass data using the $\mathbf{10-120-\oot}$ FM Higgs system in Susy SO(10) GUTs that follow the scenario\cite{blmdoom,nmsgutI} in which the $\mathbf{120}$ -plet collaborates with the $ \mathbf{10}$-plet to fit the charged fermion masses while small $\mathbf{\oot} $-plet couplings enhance the Type I seesaw neutrino masses to viable values and make the fit to light fermions accurate. Restricting ourselves to the CP conserving case we use a linear perturbative technique to obtain accurate charged fermion fits ($\chi^2_{tot} < .2 $) to all the charged fermion masses and angles. The resulting fits imply Type I neutrino masses that are generically $10^2- 10^3$ times larger than those obtained in the $\mathbf{10-\oot}$ scenario precisely because of the small $\mathbf{\oot} $ coupling. Thus the difficulty of obtaining sufficiently large neutrino masses in the context of these Next to Minimal Susy GUTs is essentially removed. The remaining free parameters allow one to obtain the correct ratio of neutrino mass squared splitting and a large($ heta_{23}^{PMNS}$) and small($ heta_{13}^{PMNS}$) mixing angle. The $ heta_{12}^{PMNS}$ is however small and this indicates that -as in the Type I $\mathbf{10-\oot}$ case - a fully realistic fit to the lepton mixing data also \emph{requires} CP violation.

Motivation & Objective

• To address the difficulty of generating sufficiently large neutrino masses in next-to-minimal SUSY SO(10) GUTs with only 10- and 126-plet Higgses.
• To achieve accurate fits to all charged fermion masses and mixing angles using a CP-conserving, linear perturbative approach.
• To demonstrate that small 126-plet couplings naturally enhance Type I seesaw neutrino masses by 10²–10³ times compared to the 10-126 scenario.
• To reproduce the correct ratio of neutrino mass squared splittings and large θ₂₃ and small θ₁₃ mixing angles in the PMNS matrix.
• To identify the necessity of CP violation for a fully realistic fit to lepton mixing data, as θ₁₂ remains small in the CP-conserving case.

Proposed method

• Utilizes a 10-120-126 Higgs representation system within a supersymmetric SO(10) Grand Unified Theory framework.
• Applies a linear perturbative technique to fit charged fermion masses and mixing angles under CP conservation.
• Introduces small couplings of the 126-plet Higgs to enhance Type I seesaw contributions to neutrino masses.
• Uses the 120-plet to fit charged fermion masses in conjunction with the 10-plet, while the 126-plet provides the dominant seesaw contribution.
• Performs a global fit to charged fermion data with χ²_total < 0.2, indicating high accuracy.
• Analyzes the resulting PMNS mixing matrix parameters, particularly θ₁₂, θ₂₃, and θ₁₃, to assess phenomenological viability.

Experimental results

Research questions

• RQ1 Can the 10-120-126 Higgs system in SUSY SO(10) GUTs achieve accurate fits to all charged fermion masses and mixing angles with χ² < 0.2 under CP conservation?
• RQ2 How do small 126-plet couplings affect the magnitude of Type I seesaw neutrino masses compared to the 10-126 scenario?
• RQ3 Does the model reproduce the correct ratio of neutrino mass squared splittings and the observed mixing angles θ₂₃ and θ₁₃?
• RQ4 Why does the model predict a small θ₁₂ in the PMNS matrix under CP conservation, and what does this imply for the need for CP violation?
• RQ5 Is CP violation necessary to achieve a fully realistic fit to lepton mixing data in this framework?

Key findings

• The model achieves a highly accurate fit to all charged fermion masses and mixing angles with a total χ² < 0.2.
• The inclusion of small 126-plet couplings enhances Type I seesaw neutrino masses by a factor of 10²–10³ compared to the 10-126 scenario, resolving a major challenge in next-to-minimal SUSY GUTs.
• The model successfully reproduces the correct ratio of neutrino mass squared splittings.
• The PMNS mixing angle θ₂₃ is predicted to be large and θ₁₃ small, consistent with experimental observations.
• The model predicts a small θ₁₂, indicating that CP violation is required to achieve a fully realistic fit to lepton mixing data.
• The framework demonstrates that the 126-plet's small couplings are sufficient to generate viable neutrino masses while maintaining consistency with charged fermion data.