Heavy Quark Masses (from QCD Sum Rules) and their impact on the (g-2)μ

We determine the charm and the bottom quark masses m(c)(m(c)) and m(b)(m(b)) from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD. Only experimental data for the heavy-quark resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to constraint the theoretical error providing a suitable parameterization of such continuum region. Our result is m(c)(m(c)) = 1272 +/- 8 MeV and m(b)(m(b)) = 4180 +/- 9MeV for alpha(s) (M-z) = 0.1182. As a byproduct, the parameterization of the ' (1) B degrees function and the heavy-quark masses are used to determine the contribution of the heavy quarks to the Hadronic Vacuum Polarization contribution to the anomalous magnetic moment of the muon yielding alpha(had,)(mu,LO) (charm) = 14.36(23) x 10(-10) and alpha(had,)(mu,LO) (charm) = 0.30 x 10(-10) respectively.