[Paper Review] Electroweak Symmetry Breaking via Bose-Einstein Mechanism

Francesco Sannino, Kimmo Tuominen|ArXiv.org|May 1, 2003

Atomic and Subatomic Physics Research3 citations

TL;DR

This paper proposes a hidden Bose-Einstein condensation mechanism as a new source of electroweak symmetry breaking, where a neutral complex scalar singlet field acquires a vacuum expectation value due to a chemical potential, indirectly triggering the Higgs mechanism via interactions with the Standard Model Higgs. The resulting corrections to dispersion relations and scattering processes are strongly suppressed by a factor of 𝜖⁴ compared to direct models, making the mechanism distinguishable from other new physics through unique, frame-dependent Lorentz-violating signatures.

ABSTRACT

Recently the Bose-Einstein phenomenon has been proposed as possible physical mechanism underlying the spontaneous symmetry breaking in cold gauge theories. The mechanism is natural and we use it to drive the electroweak symmetry breaking. It can be implemented in different ways while here we present a simple model in which the Bose-Einstein sector is felt only indirectly by all of the standard model fields. The structure of the corrections due to the new mechanism is general and independent on the model used here leading to experimental signatures which can be disentangled from other known extensions of the standard model.

Motivation & Objective

• To propose a new mechanism for electroweak symmetry breaking based on Bose-Einstein condensation in a hidden sector.
• To suppress Lorentz-violating corrections to Standard Model particles by making the Bose-Einstein sector indirectly coupled to the Higgs field.
• To identify general, model-independent experimental signatures arising from the Bose-Einstein nature of the mechanism.
• To distinguish this mechanism from other beyond-Standard-Model physics through unique dispersion relation corrections.
• To explore cosmological and phenomenological consequences of frame-dependent dispersion relations in the context of electroweak symmetry breaking.

Proposed method

• Introduce a complex scalar singlet field 𝜙 that is a singlet under all Standard Model gauge symmetries and couples to the Higgs via a renormalizable potential.
• Implement a chemical potential 𝜇 associated with a global U(1) symmetry of the Higgs field, inducing a negative tree-level mass squared for the Higgs through interactions with 𝜙.
• Use the potential V[𝜙, M] = ½(M²_H − 8ĝ|𝜙|²)Tr[M†M] + m²|𝜙|² + 𝜆̂|𝜙|⁴ + 𝜆Tr[M†M]² to generate a non-zero vacuum expectation value for 𝜙, which then induces a negative mass term for the Higgs field.
• Derive modified dispersion relations for gauge and fermion fields via one-loop corrections from the modified propagators of the Higgs and gauge bosons.
• Compute corrections to the muon decay rate and fermion velocities, showing suppression by a factor of order 𝜖⁴ compared to direct models.
• Use the general structure of the corrections to identify unique, Lorentz-violating signatures that can be disentangled from other new physics.

Experimental results

Research questions

• RQ1 Can Bose-Einstein condensation in a hidden scalar sector trigger electroweak symmetry breaking without direct coupling to the Higgs?
• RQ2 How do Lorentz-violating corrections to dispersion relations in the Standard Model fields depend on the coupling strength between the hidden Bose-Einstein sector and the Higgs?
• RQ3 What are the phenomenological consequences of the modified gauge and fermion propagators in this model?
• RQ4 Can the resulting corrections be distinguished from those of other new physics scenarios, such as supersymmetry or technicolor?
• RQ5 What is the size of the suppression factor for Lorentz-violating effects in the hidden mechanism compared to the direct mechanism?

Key findings

• The hidden Bose-Einstein mechanism induces electroweak symmetry breaking indirectly via a singlet scalar field 𝜙 that acquires a vacuum expectation value due to a chemical potential.
• The resulting corrections to the muon decay rate are suppressed by a factor of order 𝜖⁴, yielding 𝛿 ≈ 2.7×10⁻⁵ to 2.7×10⁻⁹ for ⟨|𝜙|⟩ ≈ 1–10 TeV.
• Fermion velocity corrections are further suppressed by 𝜖⁴ compared to the direct Bose-Einstein model, making them negligible at observable levels.
• The form of the dispersion relations for gauge and fermion fields is generally modified as E² = v_f²p² + m_f², with deviations from the speed of light suppressed by the coupling strength.
• The corrections are insensitive to the specific realization of the mechanism and are instead dictated solely by the Bose-Einstein nature of the condensation.
• The model produces unique, frame-dependent Lorentz-violating signatures that can be tested experimentally and distinguished from other extensions of the Standard Model.