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.

arXiv commentComments added. References added. Typos corrected. Version to be published in the Physical Review D

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Cited by in corpus (11)

• Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles
• The hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
• Lattice QCD and the anomalous magnetic moment of the muon
• Slope and curvature of the hadron vacuum polarization at vanishing virtuality from lattice QCD
• On Constraints Between $\Delta {\alpha }_{\mathrm{had}}(M_Z^2)$ and $(g_{\mu }-2{)}_{\mathrm{HVP}}$
• The Mellin-Barnes Approach to Hadronic Vacuum Polarization and $g_{\mu }-2$
• Higher-order hadronic-vacuum-polarization contribution to the muon g-2 from lattice QCD
• Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
• Anomalous magnetic moment of the muon, a hybrid approach
• Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment
• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains