[Paper Review] Unification with and without Supersymmetry: Adjoint SU(5)

P. Perez|ArXiv.org|Oct 5, 2007

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper proposes two minimal, renormalizable grand unified theories (GUTs) based on SU(5) gauge symmetry: one non-supersymmetric and one supersymmetric, both using the adjoint representation to generate neutrino masses via the type III seesaw mechanism. The models achieve unification of gauge couplings, predict one massless neutrino, and suppress proton decay through careful Higgs sector design, making them the simplest viable renormalizable SU(5) GUTs with realistic fermion masses and neutrino masses at tree level.

ABSTRACT

I present two new renormalizable grand unified theories where the neutrino masses are generated through the type I and type III seesaw mechanisms. These theories can be considered as the simplest (SUSY) renormalizable grand unified theories based on the SU(5) gauge symmetry. Several phenomenological and cosmological aspects of these proposals are discussed.

Motivation & Objective

• To construct the simplest possible renormalizable grand unified theory based on SU(5) that explains neutrino masses and fermion mass hierarchies.
• To address the failure of the Georgi-Glashow model and minimal SUSY SU(5) in reproducing charged fermion mass relations and generating massive neutrinos.
• To implement the type III seesaw mechanism using an adjoint fermion multiplet to generate neutrino masses at tree level.
• To ensure compatibility with gauge coupling unification and proton decay constraints.
• To explore phenomenological and cosmological implications, including leptogenesis and potential LHC signals of light scalar leptoquarks.

Proposed method

• Introduce a fermionic multiplet in the adjoint representation of SU(5) to mediate type III seesaw mechanism for neutrino mass generation.
• Construct a non-supersymmetric model with Higgs fields in the 5_H, 24_H, and 45_H representations to achieve fermion mass unification and neutrino masses.
• Extend the minimal SUSY SU(5) model by adding a chiral superfield in the adjoint representation and including Higgs fields in the 45_H and 24_H representations to preserve renormalizability and matter parity.
• Use matter parity conservation to forbid dangerous dimension-four proton decay operators and ensure the lightest neutralino is a viable dark matter candidate.
• Include higher-dimensional interactions via the 45_H representation to generate the correct charged fermion mass relations, avoiding the Y_E = Y_D^T problem.
• Integrate out heavy states to compute effective proton decay operators, focusing on LLLL and RRRR contributions mediated by scalar and gauge partners of the 5_H, 24_H, and 45_H multiplets.

Experimental results

Research questions

• RQ1 Can a minimal, renormalizable SU(5) GUT be constructed that generates neutrino masses via the type III seesaw mechanism at tree level?
• RQ2 How can the problematic relation Y_E = Y_D^T in minimal SU(5) GUTs be resolved while preserving renormalizability?
• RQ3 What are the proton decay rates and dominant decay channels in such a model, and can they be suppressed below current experimental bounds?
• RQ4 Can leptogenesis be realized in this framework, given the presence of one massless neutrino at tree level?
• RQ5 What are the collider signatures, such as light scalar leptoquarks, that could test this model at the LHC or future e+e− colliders?

Key findings

• The non-supersymmetric adjoint SU(5) model successfully generates neutrino masses via the type III seesaw mechanism using only the minimal Higgs sector: 5_H, 24_H, and 45_H.
• The model predicts one massless neutrino at tree level, allowing for a viable leptogenesis mechanism to explain the baryon asymmetry of the universe.
• Proton decay is suppressed through careful cancellation of dimension-five and dimension-six operators, with the dominant contributions mediated by scalar partners of the 5_H, 24_H, and 45_H multiplets.
• The supersymmetric version of the model preserves matter parity, forbids dangerous dimension-four proton decay operators, and ensures the lightest neutralino is a stable dark matter candidate.
• The model predicts the existence of light scalar leptoquarks with quantum numbers Φ_b = (3,2,1/6), which could be produced at the LHC or future e+e− colliders.
• The upper bound on the total proton decay lifetime is estimated to be τ_p^upper ≤ 2×10^36 years, making the model testable in future proton decay experiments.