Parameters
Chiral condensate:
⟨ψ̄ψ⟩ ≠ 0 breaks SU(2)_L×SU(2)_R → SU(2)_V
Goldstone bosons:
3 pions (π⁺,π⁻,π⁰) are pseudo-Nambu-Goldstone bosons: m_π² ~ m_q⟨ψ̄ψ⟩
Mexican hat:
V(σ,π) = λ(σ²+π²−v²)² − m_q σ
Minimum at σ = f_π ≈ 93 MeV
Restoration:
⟨ψ̄ψ⟩ → 0 at T_χ ≈ 155 MeV (crossover with quarks)
⟨ψ̄ψ⟩ ≠ 0 breaks SU(2)_L×SU(2)_R → SU(2)_V
Goldstone bosons:
3 pions (π⁺,π⁻,π⁰) are pseudo-Nambu-Goldstone bosons: m_π² ~ m_q⟨ψ̄ψ⟩
Mexican hat:
V(σ,π) = λ(σ²+π²−v²)² − m_q σ
Minimum at σ = f_π ≈ 93 MeV
Restoration:
⟨ψ̄ψ⟩ → 0 at T_χ ≈ 155 MeV (crossover with quarks)