Gluon condensates and precise (m)over-barc,b from QCD-moments and their ratios to order αs3 and ⟨G4⟩

We reconsider the extraction of the gluon condensates , < g(3)f(abc)G(3)> and the (MS) over bar running quark masses (m) over bar (c,b) from different M-n(Q(2)) moments and their ratios by including PT corrections to order alpha(3)(s), NPT terms up to < G(4)> and using stability criteria of the results versus the degree n (number of Q(2)-derivative). We explicitly show that the spectral part of the lowest moment M-1(0) depends strongly (as expected) on its high-energy (continuum) contribution, which is minimized for Mn >= 3-4(0). Using higher moments and the correlations of with < g(3)f(abc)G(3)> and < G(4)>, we obtain = (7.0 +/- 1.3) x 10(-2) GeV4 and < g(3)f(abc)G(3)> = (8.8 +/- 5.5) GeV2 x , while our analysis favours a modified precise factorisation for < G(4)>. Using the previous results, we re-determine (m) over bar (c)((m) over bar (c)) and find that the commonly used M-1(0) lowest moment tends to overestimate its value compared to the ones from higher moments where stable values of (m) over bar (c)((m) over bar (c)) versus the variations of n and the continuum models are reached. These features can indicate that the quoted errors of (m) over bar (c,b) from M-1(0) may have been underestimated. Our best results from different high-n moments and their ratios are: (m) over bar (c)((m) over bar (c)) = 1261(16) Mev and (m) over bar (b)((m) over bar (b)) = 4171(14) MeV, in excellent agreement with results obtained in Narison (2010) [1] using some judicious choices of ratios of moments. (C) 2011 Elsevier B.V. All rights reserved.