Gluon condensates and m¯b(m¯b) from QCD-exponential sum rules at higher orders

We test the convergence of the QCD exponential sum rules by including PT corrections to order αs3 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 〈αsG2〉 and 〈g3fabcG3〉. From charmonium systems and using the charm quark mass as input, we deduce: 〈g3fabcG3〉=(8.2±1.0) GeV2×〈αsG2〉 corresponding to 〈αsG2〉=(7.5±2.0)×10-2 GeV4. Using these results for the bottomium systems, we obtain: m¯b(m¯b)=4212(32) MeV, which is slightly higher but consistent within the errors with the ones from Q2-moments and their ratios m¯b(m¯b)=4172(12) MeV. We are tempted to consider as a final result from the sum rules approaches, the average m¯b(m¯b)=4177(11) MeV of the two previous determinations.