[Paper Review] New Ideas in Symmetry Breaking

M. Quirós|ArXiv.org|Feb 20, 2003

Black Holes and Theoretical Physics65 references19 citations

TL;DR

This paper presents novel mechanisms for symmetry breaking in higher-dimensional field theories, focusing on Scherk-Schwarz compactification, orbifolds, and the Hosotani mechanism. It demonstrates that supersymmetry and gauge symmetry can be broken via extra dimensions, with key predictions such as a heavy Higgs boson (Mh > 145 GeV) and a lower bound on the compactification scale (1/R < 10 TeV), testable at the LHC.

ABSTRACT

Some old and new ideas on symmetry breaking, based on the presence of extra dimensions that have been the subject of a very fast development and intensive studies during the last years, will be presented in these lectures. Special attention will be devoted to the various compactification mechanisms, including toroidal and orbifold compactifications, and to non-trivial boundary conditions or Scherk-Schwarz compactification. Also symmetry breaking by Wilson lines, or Hosotani breaking characteristic of non-simply connected compact manifolds will be analyzed in some detail. The different mechanisms will be applied to the breaking of the most relevant symmetries in particle physics: supersymmetry and gauge symmetry. The required background for these lectures is Quantum Field Theory, Supersymmetry and some rudiments of Kaluza-Klein theory. The different sections will be illustrated with examples.

Motivation & Objective

• To explore new mechanisms of symmetry breaking in higher-dimensional quantum field theories, particularly in the context of extra dimensions.
• To analyze how compactification on tori, orbifolds, and non-trivial boundary conditions (Scherk-Schwarz) can break gauge and supersymmetry.
• To investigate the interplay between Scherk-Schwarz breaking and the Hosotani mechanism via vacuum expectation values of gauge field components.
• To apply these mechanisms to the breaking of supersymmetry and gauge symmetry in realistic particle physics models.
• To derive phenomenologically viable predictions, such as Higgs masses and compactification scale bounds, testable at the LHC.

Proposed method

• Uses Scherk-Schwarz compactification with non-trivial boundary conditions to break symmetries in higher-dimensional theories.
• Applies orbifold compactification with fixed points to break Lorentz and gauge symmetries, introducing localized states.
• Analyzes the Hosotani mechanism, where the Wilson line of a gauge field’s extra-dimensional component acquires a vacuum expectation value.
• Reinterprets Scherk-Schwarz breaking as a form of Hosotani breaking by identifying the Scherk-Schwarz parameter with a gauge field VEV.
• Computes one-loop corrections to scalar masses (e.g., m₃²) and Yukawa couplings (λₜ) using ladder diagrams in compactified extra dimensions.
• Minimizes the one-loop effective potential to derive relations between tanβ, mₐ, and the compactification parameters ω and μ.

Experimental results

Research questions

• RQ1 How can Scherk-Schwarz breaking in extra dimensions be understood as a realization of the Hosotani mechanism?
• RQ2 What are the phenomenological consequences of supersymmetry breaking via orbifolding and Scherk-Schwarz compactification?
• RQ3 How do the masses of the Higgs bosons in a 5D model depend on the compactification parameters ω and μ?
• RQ4 What are the bounds on the compactification scale 1/R derived from electroweak precision measurements and LEP Higgs searches?
• RQ5 Can the model predict a Standard Model-like Higgs boson with mass > 145 GeV, and is it discoverable at the LHC?

Key findings

• The one-loop correction to the gaugino mass m₃² vanishes in the supersymmetric limit (ω → 0) and when μ = 0, confirming consistency with known limits.
• The model predicts a lower bound on the compactification scale of 1/R < 10 TeV, consistent with electroweak precision measurements.
• The Standard Model-like Higgs mass is bounded from below by Mₕ > 145 GeV, depending on the ω and μ parameters.
• The bound on mₐ > 95 GeV from LEP implies a lower limit on the Scherk-Schwarz parameter μ > 350 GeV.
• The model predicts a heavy Higgs sector where the Higgs boson H has suppressed couplings to Z bosons (∝ 1/tanβ), making it undetectable at LEP.
• The model is excluded if the Standard Model Higgs has a mass near 115 GeV, as such a state would be inconsistent with the predicted Mₕ > 145 GeV.