Minimum Of QCD Effective Action As Test Of QCD Confinement Parameter

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 $B_{\mu }$ = $(1+\sigma {\mathrm{\partial }}_m)A_{\mu }$ where $m$ goes to zero after differentiation, and $\sigma$ is a parameter which runs' with momentum ($k$). An exact treatment yields a structure $[1/k^2 + 2\mu^2/k^4]$ for the gluon propagator, where $\sigma^2$ =$\pi k^4/9\mu^2\alpha_s$, 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 $\mu = 1GeV$ (termed the confinement scale parameter’), in association with the QCD scale parameter ${\mathrm{\Lambda }}_{qcd}=200MeV$ [hep-ph/0109278]. This paper seeks to provide a formal basis for the ratio ${\mathrm{\Lambda }}_{qcd}\mathrm{/}\mu$ by employing the minimality condition for the $integrated$ effective action $\mathrm{\Gamma }$, 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 $\mathrm{\Gamma }$ w.r.t $S_F^{\mathrm{\prime }}$), acts as a feeder, and the stationarity condition on $\mathrm{\Gamma }$ as function of $\mu$ and ${\alpha }_s(\mu )$ gives the ratio $\mathrm{\Lambda }\mathrm{/}\mu$ = 0.246, in fair accord with the value 0.20 given above. Inclusion of a two-loop $\mathrm{\Gamma }$ is crucial for the agreement. \ Keywords: confinement scale, QCD effective action, minimality condition, $B$-field.