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
Bμ = (1+σ∂m)Aμ 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 =πk4/9μ2αs, 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
Λqcd=200MeV [hep-ph/0109278]. This paper seeks to provide a formal
basis for the ratio Λqcd/μ by employing the minimality condition
for the integrated effective action Γ, 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 SF′), acts as a feeder, and the
stationarity condition on Γ as function of μ and αs(μ)
gives the ratio Λ/μ = 0.246, in fair accord with the value 0.20
given above. Inclusion of a two-loop Γ is crucial for the agreement. \\
Keywords: confinement scale, QCD effective action, minimality condition,
B-field.Comment: LaTex file, 12 pages on dv