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 αs(M_z) = 0.1182. As a byproduct, the parameterization of the R(s) 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 a^had μ_,LO^charm = 14.36(23) × 10⁻¹⁰ and a^had μ_,LO^bottom = 0.30(2) × 10⁻¹⁰ respectively.