[Paper Review] Dynamical Origin for the 125 GeV Higgs; a Hybrid setup

Shaouly Bar-Shalom|arXiv (Cornell University)|Oct 10, 2013

Particle physics theoretical and experimental studies3 references3 citations

TL;DR

This paper proposes a hybrid electroweak symmetry breaking model combining a fundamental scalar with a Nambu-Jona-Lasinio (NJL) mechanism via a strongly coupled heavy quark sector. At a compositeness scale Λ ≈ 1 TeV, a 500 GeV doublet of heavy quarks forms a condensate, generating a composite Higgs; this is matched to a hybrid two-Higgs-doublet model (2HDM) where the fundamental scalar (mostly SM-like) and the composite scalar jointly break electroweak symmetry. The model successfully produces a 125 GeV Higgs boson with SM-like couplings, mostly fundamental in nature, while predicting a heavy CP-even Higgs at ~500 GeV and charged/psuedo-scalar Higgses at 200–300 GeV.

ABSTRACT

We describe a hybrid framework for electroweak symmetry breaking (EWSB), in which the Higgs mechanism is combined with a Nambu-Jona-Lasinio mechanism. The model introduces an unconstrained scalar (i.e., acts as "fundamental" but not the SM field) and a strongly coupled doublet of heavy quarks with a mass around 500 GeV, which forms a condensate at a compositeness scale Λ~ O(1) TeV. This setup is matched at that scale to a tightly constrained hybrid two Higgs doublet model, where both the composite and unconstrained scalars participate in EWSB. This allows us to get a good candidate for the recently observed 125 GeV scalar which has properties very similar to the Standard Model Higgs. The heavier (mostly composite) CP-even scalar has a mass around 500 GeV, while the pseudoscalar and the charged Higgs particles have masses in the range 200 -300 GeV.

Motivation & Objective

• To address the hierarchy problem and extend the Standard Model beyond the 125 GeV Higgs discovery by proposing a dynamical electroweak symmetry breaking (DEWSB) mechanism.
• To reconcile a light 125 GeV Higgs with strong dynamics, avoiding the fine-tuning issues of top-condensation models.
• To construct a viable framework where the observed Higgs is predominantly fundamental but arises in a composite sector, preserving SM-like couplings.
• To explore a hybrid setup where both fundamental and composite scalars contribute to electroweak symmetry breaking, consistent with LHC data and precision electroweak constraints.
• To identify a viable parameter space with a 125 GeV Higgs, a heavy CP-even Higgs at ~500 GeV, and charged/psuedo-scalar Higgses at 200–300 GeV.

Proposed method

• Introduces a fundamental scalar field (Φℓ) and a strongly coupled heavy quark doublet (ψ) with mass ~500 GeV, forming a condensate at Λ ~ 1 TeV via an effective 4-Fermi interaction Lagrangian, L_NJL = Gψ (ψ̄LψR)(ψ̄RψL).
• Uses an auxiliary scalar field H to reproduce the 4-Fermi interaction upon integration, with H interpreted as the composite scalar bound state H ~ <ψ̄ψ>.
• Matches the composite sector at scale Λ to a hybrid two-Higgs-doublet model (h4G2HDM), where Φℓ couples to light SM fermions and the composite field Φh couples to the heavy 4th generation fermions.
• Solves the renormalization group equations (RGEs) for couplings gq′ and λh, showing that λℓ(Λ) → 0 is required for a light Higgs, implying Φℓ is a pseudo-Goldstone boson of the underlying strong dynamics.
• Derives physical Higgs masses using m_h,H² = (m₁² + m₂² ∓ √((m₁² - m₂²)² + 4μ_hℓ⁴))/2, with m₁² ≈ tβμ_hℓ² + sβ²v²λh/2 and m₂² ≈ μ_hℓ²/tβ + cβ²v²λℓ/2.
• Determines the Higgs mixing angle via tan 2α ≈ (cot 2β - v²(sβ²λh - cβ²λℓ)/(2μ_hℓ²))⁻¹, showing small mixing (α ~ O(1)) when λℓ(Λ) → 0, ensuring the 125 GeV state is mostly fundamental.

Experimental results

Research questions

• RQ1 Can a light 125 GeV Higgs arise in a composite Higgs framework without fine-tuning, while preserving SM-like couplings?
• RQ2 How can a fundamental-like scalar coexist with a composite scalar in a unified EWSB mechanism?
• RQ3 What is the role of a 500 GeV heavy quark doublet in generating a viable Higgs sector with a light Higgs and heavier Higgs states?
• RQ4 How does the requirement λℓ(Λ) → 0 at the compositeness scale affect the Higgs mass spectrum and mixing?
• RQ5 What are the viable parameter ranges for tanβ and mA that yield a 125 GeV Higgs consistent with LHC data and electroweak precision observables?

Key findings

• A 125 GeV Higgs boson is obtained when the fundamental scalar's quartic coupling λℓ(Λ) → 0 at the compositeness scale, implying it behaves as a pseudo-Goldstone boson.
• The light Higgs (h) is predominantly fundamental, with mixing angle α ~ O(1), ensuring it has SM-like couplings to gauge bosons and fermions.
• The heavy CP-even Higgs (H) has a mass of approximately 500 GeV, arising from the composite sector with m_H ~ v√(λh/2), and is mostly composed of the composite scalar.
• The charged Higgs (H⁺) and pseudoscalar (A) have masses in the range 200–300 GeV, consistent with current LHC constraints.
• The compositeness scale is Λ ≈ 1–1.5 TeV for m_q′ ≈ 500 GeV and tanβ ~ O(1), avoiding the 10¹⁷ GeV cutoff of top-condensation models and eliminating fine-tuning.
• The model reproduces all measured 125 GeV Higgs signal strengths and is consistent with electroweak precision data, as confirmed by full RGE analysis and numerical validation.