[Paper Review] Fermion masses and proton decay in string-inspired SU(4)×SU(2)2×U(1)XSU(4)×SU(2)2×U(1)X

T. Dent, G.K. Leontaris+1 more|arXiv (Cornell University)|Jan 13, 2005

Particle physics theoretical and experimental studies5 citations

TL;DR

This paper proposes a supersymmetric SU(4)×SU(2)₂×U(1)X model with matter in fundamental and antisymmetric tensor representations, using distinct Clebsch–Gordan coefficients for up, down, charged lepton, and neutrino Yukawa matrices to generate hierarchical fermion masses and bi-large neutrino mixing. The model achieves anomaly cancellation via a Green–Schwarz mechanism with fractional U(1)X charges, successfully suppressing proton decay at dimension-4 and -5 levels.

ABSTRACT

We present a supersymmetric model of fermion masses with SU(4)×SU(2)2×U(1)XSU(4)×SU(2)2×U(1)X gauge group with matter in fundamental and antisymmetric tensor representations only. The up, down, charged lepton and neutrino Yukawa matrices are distinguished by different Clebsch–Gordan coefficients due to contracting over SU(4)SU(4) and SU(2)RSU(2)R indices. We obtain a hierarchical light neutrino mass spectrum with bi-large mixing. The condition that anomalies be cancelled by a Green–Schwarz mechanism leads to fractional U(1)XU(1)X charges which exclude B violation through dimension-4 and -5 operators.

Motivation & Objective

• To construct a supersymmetric grand unified theory based on SU(4)×SU(2)₂×U(1)X with minimal matter representations.
• To explain the hierarchical structure of fermion masses and the bi-large mixing pattern in neutrinos.
• To ensure anomaly cancellation through a Green–Schwarz mechanism with fractional U(1)X charges.
• To suppress proton decay by excluding dimension-4 and dimension-5 B-number violating operators.

Proposed method

• Employing fundamental and antisymmetric tensor representations for matter fields under SU(4)×SU(2)₂×U(1)X.
• Using different Clebsch–Gordan coefficients for SU(4) and SU(2)R indices to distinguish Yukawa matrices for up-type quarks, down-type quarks, charged leptons, and neutrinos.
• Implementing a Green–Schwarz mechanism to cancel gauge anomalies, leading to fractional U(1)X charges.
• Analyzing the resulting effective Lagrangian to assess the presence of dimension-4 and dimension-5 operators violating baryon number.
• Evaluating the neutrino mass spectrum and mixing angles from the structure of the neutrino Yukawa matrix.
• Ensuring consistency with observed fermion mass hierarchies and neutrino oscillation data.

Experimental results

Research questions

• RQ1 How can a unified model with SU(4)×SU(2)₂×U(1)X gauge symmetry generate hierarchical fermion masses?
• RQ2 What determines the bi-large mixing pattern observed in neutrino oscillations within this model?
• RQ3 Can the Green–Schwarz mechanism in this model lead to fractional U(1)X charges that suppress proton decay?
• RQ4 Are dimension-4 and dimension-5 baryon number violating operators excluded in this framework?
• RQ5 How do the Clebsch–Gordan coefficients for SU(4) and SU(2)R differially affect the Yukawa matrices?

Key findings

• The model successfully generates a hierarchical light neutrino mass spectrum consistent with neutrino oscillation data.
• Bi-large mixing in the neutrino sector arises naturally from the structure of the neutrino Yukawa matrix and Clebsch–Gordan coefficients.
• Anomaly cancellation via the Green–Schwarz mechanism leads to fractional U(1)X charges, which are essential for suppressing proton decay.
• The presence of fractional U(1)X charges excludes dimension-4 and dimension-5 operators that violate baryon number, thus stabilizing the proton.
• The model uses only fundamental and antisymmetric tensor representations, minimizing the spectrum while preserving phenomenological viability.
• The distinct Yukawa matrices for up-type quarks, down-type quarks, charged leptons, and neutrinos are determined by different group-theoretic contractions over SU(4) and SU(2)R indices.