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We discuss a new technique to evaluate integrals of QCD Green's functions inthe Euclidean based on their Mellin-Barnes representation. We present as afirst application the evaluation of the lowest order Hadronic VacuumPolarization (HVP) contribution to the anomalous magnetic moment of the muon$\frac{1}{2}(g_{\mu}-2)_{\rm\tiny HVP}\equiv a_{\mu}^{\rm HVP}$. It is shownthat with a precise determination of the slope and curvature of the HVPfunction at the origin from lattice QCD (LQCD), one can already obtain a resultfor $a_{\mu}^{\rm HVP}$ which may serve as a test of the determinations basedon experimental measurements of the $e^+ e^-$ annihilation cross-section intohadrons.

Hadronic Vacuum Polarization in QCD and its Evaluation in the Euclidean