[Paper Review] Finite Unification: Theory, Models and Predictions

S. Heinemeyer, M. C. Mondragon+1 more|arXiv (Cornell University)|Jan 13, 2011

Particle physics theoretical and experimental studies1 references4 citations

TL;DR

This paper proposes finite unified theories (FUTs) within N=1 supersymmetric Grand Unified Theories (GUTs), achieving all-loop finiteness via renormalization group invariant (RGI) relations among couplings. By enforcing RGI conditions on gauge, Yukawa, and soft-breaking parameters, the models predict a light Higgs mass and top quark mass consistent with LHC data, with the SU(3)³ model showing viable parameter regions near r ≈ 0.5–0.62 for both top and bottom quark masses under updated thresholds.

ABSTRACT

All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) realising an old field theory dream, and moreover have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensional couplings that guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory, too. Based on the above theoretical framework phenomenologically consistent FUTs have been constructed. Here we review FUT models based on the SU(5) and SU(3)^3 gauge groups and their predictions. Of particular interest is the Higgs mass prediction of the models which is expected to be tested at the LHC.

Motivation & Objective

• To develop N=1 supersymmetric Grand Unified Theories (GUTs) that are finite to all orders in perturbation theory.
• To extend the reduction of couplings beyond gauge and Yukawa sectors into the soft supersymmetry breaking sector via RGI relations.
• To construct phenomenologically viable FUT models based on SU(5) and SU(3)³ gauge groups with testable predictions.
• To predict the Higgs boson mass and supersymmetric spectrum, testable at the LHC.
• To reconcile finiteness with realistic fermion masses and B-physics constraints.

Proposed method

• Implement RGI relations among dimensionless couplings (gauge and Yukawa) to enforce all-loop finiteness in N=1 SUSY GUTs.
• Extend RGI conditions to dimensionful soft-breaking parameters, ensuring finiteness in the soft sector as well.
• Construct FUT models based on SU(5) and SU(3)³ gauge groups with specific representations and mass spectra.
• Use two-loop renormalization group equations to analyze fermion masses and constrain model parameters like r and μ.
• Incorporate new thresholds for exotic particles (e.g., h and E states) decoupling below M_GUT to widen viable parameter space.
• Apply experimental constraints from top and bottom quark masses, B-physics, and Higgs mass limits to select phenomenologically viable models.

Experimental results

Research questions

• RQ1 Can RGI relations among couplings in N=1 SUSY GUTs lead to all-loop finiteness in both gauge and soft-breaking sectors?
• RQ2 What are the viable parameter regions in SU(3)³ FUT models that reproduce the observed top and bottom quark masses?
• RQ3 How do new exotic particle thresholds below M_GUT affect the phenomenological viability of FUT models?
• RQ4 What is the predicted Higgs boson mass in finite unified models, and is it testable at the LHC?
• RQ5 Can the FUT framework simultaneously predict the top quark mass and satisfy B-physics constraints?

Key findings

• The SU(3)³ FUT model with μ < 0 allows a viable parameter region at r ≈ 0.5–0.62 where both top and bottom quark masses are consistent with experimental data.
• For the two-loop SU(3)³ model with μ < 0, the bottom quark mass constraint yields r ≈ 0.62–0.77, while the top quark mass constraint gives r ≈ 0.4–0.62, indicating a narrow but viable overlap.
• Including a down-like exotic particle decoupling at 10¹⁴ GeV widens the viable parameter space, allowing consistent agreement with data at r ≈ 0.5–0.62.
• The model predicts a light Higgs boson mass that is expected to be tested at the LHC within the next few years.
• The FUT framework successfully predicts the top quark mass, extending the success of earlier RGI-based models.
• The red points in Fig. 5, satisfying B-physics constraints, cluster around r ≈ 0.5–0.62, confirming phenomenological viability under updated thresholds.