Light-by-light forward scattering amplitudes in Lattice QCD

TL;DR

This paper reports preliminary lattice QCD calculations of light-by-light scattering amplitudes, linking them to meson-photon interactions and aiding the understanding of muon g-2 contributions.

Contribution

It introduces a lattice QCD approach to compute light-by-light scattering amplitudes and connects these to phenomenological meson-photon interactions.

Findings

Few states suffice to reproduce the data.

Sum rules relate meson-photon couplings and form factors.

Results provide insights into meson contributions to muon g-2.

Abstract

We present our preliminary results on the calculation of hadronic light-by-light forward scattering amplitudes using vector four-point correlation functions computed on the lattice. Using a dispersive approach, forward scattering amplitudes can be described by $\gamma^* \gamma^* \to$ hadrons fusion cross sections and then compared with phenomenology. We show that only a few states are needed to reproduce our data. In particular, the sum rules considered in this study imply relations between meson$-\gamma\gamma$ couplings and provide valuable information about individual form factors which are often used to estimate the meson-pole contributions to the hadronic light-by-light contribution to the $(g-2)$ of the muon.