Hadronic light-by-light scattering contribution to the muon g – 2 on the lattice

Abstract

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g̅2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor Fπ0γ*γ* (q21; q21) in the spacelike region with photon virtualities up to 1.5 GeV2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by γ*γ* → hadrons fusion cross sections and then compared with phenomenological models.