Gluon Condensates and mb(mb) from QCD-Exponential Moments at Higher Orders
Abstract
We test the convergence of the QCD exponential moments by including PT corrections to order αs3 and the NP contributions up to D=8 <G4> 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 <αs G2> and < g3fabc G3>. From charmonium systems and using the charm quark mass as input, we deduce:< g3fabc G3> =(8.2+-1.0)GeV2 <αs G2> corresponding to < αs G2>=(7.5+- 2.0) 10-2 GeV4. Using these results for the bottomium systems, we obtain: mb(mb)= 4212(32) MeV, which is slightly higher but consistent within the errrors with the ones from Q2-moments and their ratios: mb(mb)= 4172(12) MeV. We are tempted to consider as a final result from the sum rules approaches, the average mb(mb)= 4177(11) MeV of the two previous determinations.
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