QCD Sum Rules

Abstract

The coupling constant g in the gluon tensor G ^a _µv = ∂ _µ A ^a _v −∂ _v A ^a _µ + gf^abcA ^b _µ A ^c _v is a bare one. Actually, all physical processes are described by the running or effective coupling α _s (Q²) ≡ g²(Q²)/4π, characterizing interactions at momenta Q², where Q² = −q² (at distances r ≈ Q⁻¹). The asymptotic freedom (Politzer, 1973; Gross and Wilzcek, 1973) takes place for α _s (Q²) ≈ 2π/(9 ln Q/Λ) (for 3 flavours). Because of logarithmic fall off of the coupling the structure of the theory at short distance is simple; the dynamical analysis can be carried out in terms of quarks and gluons interacting perturbatively. Here more or less the same logarithims occur as in electrodynamics. The genuine hadronic theory starts at a length of 0.5 fm and larger.