Hadronic Vacuum Polarization in QCD and its Evaluation in the Euclidean

Abstract

We discuss a new technique to evaluate integrals of QCD Green's functions in the Euclidean based on their Mellin-Barnes representation. We present as a first application the evaluation of the lowest order Hadronic Vacuum Polarization (HVP) contribution to the anomalous magnetic moment of the muon $\frac{1}{2}(g_{\mu }-2{)}_{\mathrm{HVP}}\equiv a_{\mu }^{\mathrm{HVP}}$. It is shown that with a precise determination of the slope and curvature of the HVP function at the origin from lattice QCD (LQCD), one can already obtain a result for $a_{\mu }^{\mathrm{HVP}}$ which may serve as a test of the determinations based on experimental measurements of the $e^{+}{e}^{-}$ annihilation cross-section into hadrons.

Comments: Comments added. References added. Typos corrected. Version to be published in the Physical Review D