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We test the convergence of the QCD exponential moments by including PTcorrections to order \alpha_s^3 and the NP contributions up to D=8 <G^4>condensates. Then, using the ratio of exponential sum rules where the QCD PTseries is more convergent, we study the correlation between the gluoncondensates <\alpha_s G^2> and < g^3f_{abc} G^3>. From charmonium systems andusing the charm quark mass as input, we deduce:< g^3f_{abc} G^3>=(8.2+-1.0)GeV^2 <\alpha_s G^2> corresponding to < \alpha_s G^2>=(7.5+- 2.0)10^{-2} GeV^4. Using these results for the bottomium systems, we obtain:m_b(m_b)= 4212(32) MeV, which is slightly higher but consistent within theerrrors with the ones from Q^2-moments and their ratios: m_b(m_b)= 4172(12)MeV. We are tempted to consider as a final result from the sum rulesapproaches, the average m_b(m_b)= 4177(11) MeV of the two previousdeterminations.

Gluon Condensates and m_b(m_b) from QCD-Exponential Moments at Higher Orders