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

TL;DR

This paper reviews lattice QCD approaches to calculating the hadronic light-by-light scattering contribution to the muon g-2, including position-space methods, pion transition form factors, and scattering amplitudes, advancing theoretical precision.

Contribution

It introduces new lattice techniques for HLbL calculations, including a position-space approach and computations of the pion transition form factor, enhancing the understanding of muon g-2 contributions.

Findings

Exploratory studies of pion-pole contribution in a simple model.

Lattice calculation of the pion transition form factor up to 1.5 GeV^2.

Lattice evaluation of HLbL forward scattering amplitudes.

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 g-2, 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 F_{pi^0 gamma^* gamma^*}(q_1^2, q_2^2) in the spacelike region with photon virtualities up to 1.5 GeV^2 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 gamma^* gamma^* -> hadrons fusion cross sections and then compared with phenomenological models.