M U + M D from Qcd-hadron Duality

The value of the light quark masses combination mu + md is analized using QCD-Hadron Duality. A detailed analysis of both the perturbative QCD [to four-loops] and the hadronic parametrization needed is done. The result we get is [mu+md](1GeV ) = (12.8±2.5) MeV ([mu+md](4GeV ) = (9.8 ± 1.9) MeV ) in the MS scheme. August 1997 Work supported in part by CICYT Grant No. AEN-96/1672 (Spain). Invited talk at “High Energy Conference on Quantum Chromodynamics (QCD ’97)”, 3-9 July 1997, Montpellier, France. We are interested in the value of the light quark masses that appear in the Standard Model. These are the QCD Lagrangian quark masses or Current Algebra quark masses. This work is an update of [1] putting some emphasis in the QCD-Hadron Duality and including the recently calculated α s QCD corrections [2]. A collection of the relevant references to earlier work can be found in [1]. The QCD Sum Rule (SR) technique has been discussed several times in this conference. (See the talks by Narison and Jamin for instance.) The relevant two-point function for calculating mu + md is the correlator of two divergences of the axial-vector current with the quantum numbers of the pion field