Gluon condensates and (m)over-barb ((m)over-barb) from QCD-exponential sum rules at higher orders

We test the convergence of the QCD exponential sum rules by including PT corrections to order alpha(3)(s) and the NP contributions up to dimension D = 8 condensates. Then, using the ratio of exponential sum rules where the QCD PT series is more convergent, we study the correlation between the gluon condensates and < g(3) f(abc)G(3)>. From charmonium systems and using the charm quark mass as input, we deduce: < g(3)f(abc)G(3)> = (8.2 +/- 1.0) GeV2 x (alpha(s)G(2)) corresponding to = (7.5 +/- 2.0) x 10(-2) GeV4. 'Jsing these results for the bottomium systems, we obtain: (m) over bar (b)((m) over bar (b)) = 4212(32) MeV, which is slightly higher but consistent within the errors with the ones from Q(2)-moments and their ratios (m) over bar (b)((m) over bar (b)) = 4172(12) MeV. We are tempted to consider as a final result from the sum rules approaches, the average (m) over bar (b)((m) over bar (b)) = 4177(11) MeV of the two previous determinations. (C) 2011 Elsevier B.V All rights reserved.