Wilson's Effective Field Theory

Wilson's approach: integrate out modes above a cutoff Λ to get a low-energy EFT. Couplings run with the RG scale μ via beta functions. Relevant operators (d < 4) grow at low energy; irrelevant operators (d > 4) are suppressed by powers of (E/Λ). Marginal operators (d = 4) run logarithmically.

Running Couplings

Operator Hierarchy

EFT Flow

— Marginal g (QCD-like) — Relevant m² (mass) — Irrelevant λ₆ (dim 6)

UV coupling g₀

0.50

Beta coeff b₀

−1.5

UV cutoff Λ (TeV)

Anomalous dim γ

0.10

IR scale μ_IR (GeV)

1.0