Gluon condensates and c, b quark masses from quarkonia ratios of moments

We extract (for the first time) the ratio of the gluon condensate < g(3)f(abc)G(3)>/(alpha(s)G(2)) expressed in terms of the liquid instanton radius p(c) from charmonium moments sum rules by examining the effects of (alpha(s)G(2)) in the determinations of both p(c) and the running mass (m) over bar (c)(m(c)). Using a global analysis of selected ratios of moments at different Q(2) = 0, 4m(c)(2) and 8m(c)(2) and keeping (alpha(s)G(2)) from 0.06 GeV4, where the estimate of rho(c) is almost independent of (alpha(s)G(2)), we deduce: rho(c) = 0.98(21) GeV-1 corresponding to (g(3)f(abc)G(3)) = (31 +/- 13) GeV2(alpha(s)G(2)). The value of (m) over bar (c)(mc) is less affected (within the errors) by the variation of (alpha(s)G(2)), where a common solution from different moments are reached for (alpha(s)G(2)) >= 0.02 GeV4. Using the values of (alpha(s)G(2)) = 0.06(2) GeV4 from some other channels and the previous value of (g(3)f(abc)G(3)), we deduce: (m) over bar (c)(m(c)) = 1261(18) MeV and (m) over bar (b)(m(b)) = 4232(10) MeV, where an estimate of the 4-loops (O(alpha(3)(s))) contribution has been included. Our analysis indicates that the errors in the determinations of the charm quark mass and of as without taking into account the ones of the gluon condensates have been underestimated. To that accuracy, one can deduce the running light and heavy quark masses and their ratios evaluated at M-Z. where it is remarkable to notice the approximate equalities: m(s)/m(u) approximate to m(b)/m(s) approximate to m(b)/m(s) approximate to m(t)/m(b) approximate to 51(9), which might reveal some eventual underlying novel symmetry of the quark mass matrix in some Grand Unified Theories. (C) 2010 Elsevier B.V. All rights reserved.