Hadronic vacuum polarization in QCD and its evaluation in Euclidean spacetime

Eduardo de Rafael (1, 2)

1 CPT - E1 Physique des particules
2 CPT - Centre de Physique Théorique - UMR 7332

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 bfor $a_{\mu}^{\rm HVP}$ which may serve as a test of the determinations based on experimental measurements of the $e^+ e^-$ annihilation cross-section into hadrons.

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]; Physique des Hautes Energies - Réseau [hep-lat]

Eduardo de Rafael. Hadronic vacuum polarization in QCD and its evaluation in Euclidean spacetime. Physical Review D, 2017, 96 (1), pp.014510 ⟨10.1103/PhysRevD.96.014510⟩. ⟨hal-01481059⟩