# Hadronic Vacuum Polarization in QCD and its Evaluation in the Euclidean

## TL;DR

This paper introduces a new Euclidean-space technique using Mellin-Barnes representation to evaluate QCD Green's function integrals, applied here to compute the muon's anomalous magnetic moment contribution from Hadronic Vacuum Polarization, linking lattice QCD results with experimental data.

## Contribution

The paper presents a novel method for evaluating QCD Green's function integrals in Euclidean space, enabling a new approach to calculating the muon's anomalous magnetic moment from lattice QCD data.

## Key findings

- Demonstrated the method's application to HVP contribution to muon g-2.
- Showed that lattice QCD data can provide a test for experimental determinations.
- Achieved a preliminary estimate of a_mu^HVP using the new technique.

## 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 $\frac{1}{2}(g_{\mu}-2)_{\rm\tiny HVP}\equiv a_{\mu}^{\rm HVP}$. 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 $a_{\mu}^{\rm HVP}$ which may serve as a test of the determinations based on experimental measurements of the $e^+ e^-$ annihilation cross-section into hadrons.