QCD Chiral Symmetry
QCD has an approximate SU(2)_L × SU(2)_R chiral symmetry when quark masses are small. The QCD vacuum spontaneously breaks this to SU(2)_V — generating the quark condensate ⟨q̄q⟩ ≠ 0.
Chiral Lagrangian:
V(σ,π) = λ(σ²+π²-v²)²/4
- hσ (explicit breaking)
Order parameter: ⟨q̄q⟩ ≠ 0
Goldstone bosons (mq→0):
3 pions (π⁰, π±) m≈140 MeV
"Pseudo-Goldstone" for mq≠0
GOR relation:
mπ² fπ² = -mq⟨q̄q⟩
fπ ≈ 93 MeV (pion decay const)
Chiral restoration: T > Tc ≈ 155 MeV
(quark-gluon plasma transition)
The spontaneous breaking gives quarks constituent masses ~350 MeV even when the current mass is only ~5 MeV — this explains most of the proton's mass.
Computing...