Minimum of QCD effective action as test of QCD confinement parameter

Abstract

A new approach to the non-perturbative regime of QCD is proposed by introducing a (non-hermitian) field B related to the usual gluon field A by B_μ = (1+σ∂_m)A_μ where m goes to zero after differentiation, and σ is a parameter which 'runs' with momentum |(k). An exact treatment yields a structure [1/k² + 2μ²/k⁴] for the gluon propagator, where |σ² = πk⁴/9μ²s, showing linear confinement in the instantaneous limit. This propagator was recently employed to evaluate some basic condensates and their temperature dependence (in the cosmological context), which were all reproduced for μ = 1GeV (termed the 'confinement scale parameter'), in association with the QCD scale parameter Λ_qcd = 200MeV [hep-ph/0109278]. This paper seeks to provide a formal basis for the ratio Λ_qcd/μ by employing the minimality condition for the integrated effective action, up to the 2-loop level, using the Cornwall-Jackiw formalism for composite operators. To that end the mass function m(p), determined via the Schwinger-Dyson equation (as a zero of the functional derivative of Γ w.r.t S'_F), acts as a feeder, and the stationarity condition on Γ as function of μ and α_s(μ) gives the ratio Λ/μ = 0.246, in fair accord with the value 0.20 given above. Inclusion of a two-loop is crucial for the agreement.