[Paper Review] A Road to the Standard Grand Unified Theory

Nobuhiro Maekawa|arXiv (Cornell University)|Oct 22, 2001

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes a natural SO(10) Grand Unified Theory (GUT) framework where doublet-triplet splitting is achieved via the Dimopoulos-Wilczek mechanism, leading to realistic quark and lepton mass matrices with bi-maximal neutrino mixing. The inclusion of all symmetry-allowed interactions and a fixed U(1)_A charge assignment uniquely determines all mass scales, including the GUT scale and superheavy particle masses, with automatic suppression of flavor-changing neutral currents in an E_6 extension.

ABSTRACT

In this talk, we propose a GUT scenario in which doublet-triplet splitting is naturally realized in SO(10) unification using the Dimopoulos-Wilczek mechanism and the realistic mass matrices of quarks and leptons are obtained in a simple way. For the neutrino sector, bi-maximal neutrino mixing angles are realized. Moreover, the generic interaction is allowed, namely, all the terms which are allowed by the symmetry are included in the scenario. Therefore, once we fix the integer number charges of the anomalous U(1)_A symmetry, which plays an essential role in the scenario, all the scales, GUT breaking scale, mass scales of superheavy particles, are determined. The scenario can be extended into E_6 unification, in which a condition for suppression of flavor changing neutral current (FCNC) is automatically satisfied.

Motivation & Objective

• To construct a realistic Grand Unified Theory within SO(10) that naturally realizes doublet-triplet splitting.
• To achieve realistic quark and lepton mass matrices with bi-maximal neutrino mixing angles.
• To determine all mass scales uniquely through the integer charge assignment of an anomalous U(1)_A symmetry.
• To extend the framework to E_6 unification while automatically suppressing flavor-changing neutral currents (FCNC).
• To ensure all symmetry-allowed interactions are included, making the model predictive and minimal in structure.

Proposed method

• Employ the Dimopoulos-Wilczek mechanism to dynamically achieve doublet-triplet splitting in SO(10) GUT.
• Use a U(1)_A symmetry with fixed integer charges to constrain the vacuum expectation values and fix all mass scales.
• Include all symmetry-allowed terms in the Lagrangian to ensure a generic and predictive framework.
• Construct quark and lepton mass matrices that reproduce observed fermion masses and mixing patterns.
• Extend the model to E_6 unification, where the same U(1)_A structure naturally suppresses FCNCs.
• Derive the GUT scale and superheavy particle masses as direct consequences of the U(1)_A charge assignment.

Experimental results

Research questions

• RQ1 How can doublet-triplet splitting be naturally realized in an SO(10) GUT without fine-tuning?
• RQ2 What mechanism allows for realistic quark and lepton mass matrices with bi-maximal neutrino mixing?
• RQ3 How do the integer charges of the anomalous U(1)_A symmetry determine all mass scales in the model?
• RQ4 Can the inclusion of all symmetry-allowed interactions lead to a predictive and consistent GUT framework?
• RQ5 Does the E_6 extension of the model automatically suppress flavor-changing neutral currents?

Key findings

• The doublet-triplet splitting is naturally achieved through the Dimopoulos-Wilczek mechanism in SO(10) GUT.
• Realistic quark and lepton mass matrices are obtained with bi-maximal neutrino mixing angles.
• All mass scales, including the GUT scale and superheavy particle masses, are uniquely determined by the integer U(1)_A charge assignment.
• The inclusion of all symmetry-allowed interactions leads to a fully predictive model with no free parameters beyond the U(1)_A charges.
• The E_6 extension of the model automatically satisfies the condition for suppression of flavor-changing neutral currents.
• The model's predictivity and consistency are ensured by the symmetry structure and the fixed U(1)_A charges.