Chiral Symmetry Breaking

Quark Condensate and the QCD Vacuum
Mexican Hat Potential V(σ,π)
Phase Diagram: ⟨ψ̄ψ⟩ vs Temperature
Pion as Pseudo-Goldstone Boson

Chiral Symmetry Breaking

QCD with massless quarks has chiral symmetry SU(Nf)L×SU(Nf)R. The QCD vacuum spontaneously breaks this to SU(Nf)V via a quark condensate ⟨ψ̄ψ⟩ ≠ 0.

The order parameter follows a Mexican hat potential. Goldstone's theorem predicts Nf²−1 massless bosons (pions), which gain small mass from explicit breaking by quark masses.

At T > Tχ ≈ 150 MeV, chiral symmetry restores: ⟨ψ̄ψ⟩ → 0.

⟨ψ̄ψ⟩ = 0.95 fπ
mπ ≈ 140 MeV (explicit breaking)