Quark Condensate from Renormalization Group Optimized Spectral Density

Our renormalization group consistent variant of optimized perturbation, RGOPT, is used to calculate the nonperturbative QCD spectral density of the Dirac operator and the related chiral quark condensate 〈q‾q〉, for nf=2 and nf=3 massless quarks. Sequences of approximations at two-, three-, and four-loop orders are very stable and give 〈q‾q〉nf=21/3(2GeV)=−(0.833−0.845)Λ‾2, and 〈q‾q〉nf=31/3(2GeV)=−(0.814−0.838)Λ‾3 where the range is out estimated theoretical error and Λ‾nf the basic QCD scale in the MS¯-scheme. We compare those results with other recent determinations (from lattice calculations and spectral sum rules).