[Paper Review] Reduction of couplings and its application in particle physics, Finite theories, Higgs and top mass predictions

S. Heinemeyer, Jisuke Kubo+5 more|arXiv (Cornell University)|Nov 26, 2014

Particle physics theoretical and experimental studies3 references5 citations

TL;DR

This paper presents the reduction of couplings as a scheme-independent method in quantum field theory that constrains multiple couplings through a single primary coupling via renormalization group equations. It enables precise predictions of the top and Higgs masses in the Standard Model and supersymmetric extensions, successfully forecasting the Higgs boson mass near 121–126 GeV before its discovery, and identifies supersymmetry as a key framework for finiteness and consistency with experimental data.

ABSTRACT

In this report we tell the story of the notion "reduction of couplings" as we witnessed it in the course of time. Born as an innocent child of renormalization theory it first served the study of asymptotic behavior of several couplings in a given model. Reduced couplings appeared as functions of a primary one, compatible with the renormalization group equation and thus solutions of a specific set of ordinary differential equations. If these functions have the form of power series the respective theories resemble standard renormalizable ones and thus widen considerably the area covered until then by symmetries as a tool for constraining the number of couplings consistently. Still on the more abstract level reducing couplings enabled one to construct theories with beta-functions vanishing to all orders of perturbation theory. Reduction of couplings became physicswise truely interesting and phenomenologically important when applied to the standard model and its possible extensions. In particular in the context of supersymmetric theories it became the most powerful tool known today once it was learned how to apply it also to couplings having dimension of mass and to mass parameters. Technically this all relies on the basic property that reducing couplings is a renormalization scheme independent procedure. Predictions of top and Higgs mass prior to their experimental finding highlight the fundamental physical significance of this notion. Twenty-two original articles and one set of lectures are being commented, put into historical perspective and interrelated with each other.

Motivation & Objective

• To establish reduction of couplings as a scheme-independent, symmetry-free method for constraining multiple couplings in quantum field theories.
• To apply this method to the Standard Model and its extensions to predict the top and Higgs boson masses prior to experimental discovery.
• To explore how finiteness and vanishing beta-functions in supersymmetric theories can be achieved through coupling reduction.
• To reconcile finite unified models with low-energy phenomenology and LHC data, particularly the Higgs boson mass.
• To investigate whether the success of coupling reduction points toward supersymmetry as the underlying symmetry of nature.

Proposed method

• Utilizes renormalization group equations (RGEs) to express multiple couplings as functions of a single primary coupling, ensuring consistency across energy scales.
• Applies the reduction principle to couplings with mass dimensions and mass parameters, extending its validity beyond pure coupling constants.
• Employs scheme independence of the reduction procedure to ensure physical predictions are robust under renormalization scheme changes.
• Combines reduction with finiteness conditions in N=1 supersymmetric gauge theories to achieve all-order vanishing beta-functions.
• Uses perturbative unification of gauge and Yukawa couplings in supersymmetric GUTs to constrain soft-breaking terms and predict sparticle masses.
• Performs global fits of the reduced theory to low-energy data and LHC Higgs mass measurements to test consistency and predict the lightest Higgs state.

Experimental results

Research questions

• RQ1 Can the reduction of couplings method predict the top and Higgs boson masses with high precision before experimental observation?
• RQ2 How does the reduction of couplings procedure remain scheme-independent and thus physically meaningful across different renormalization schemes?
• RQ3 To what extent can finite supersymmetric models with vanishing beta-functions be consistent with the observed Higgs boson mass?
• RQ4 Can the reduction of couplings in the MSSM and its extensions reproduce the experimentally measured Higgs mass and identify it as the SM Higgs?
• RQ5 Does the success of coupling reduction in predicting key particle masses point toward supersymmetry as the fundamental underlying symmetry?

Key findings

• The reduction of couplings predicted a top quark mass of approximately 178.8 GeV in finite SU(5) supersymmetric models, remarkably close to the later experimental value.
• In the minimal supersymmetric standard model (MSSM), the method led to a prediction of the Higgs boson mass in the range 121–126 GeV, consistent with the LHC discovery.
• The lightest Higgs boson in the MSSM was identified as the discovered Higgs-like particle through partial reduction, confirming consistency with the Standard Model.
• The method showed that asymptotic freedom in the SM requires the top quark mass to be above roughly 111 GeV, with predictions highly sensitive to the number of fermion generations.
• Cancellation of quadratic divergences was found to be incompatible with the asymptotic freedom bound, suggesting supersymmetry as a natural solution.
• Finite unified models based on reduction of couplings successfully predicted key particle masses and provided a framework for testing supersymmetry at colliders.