Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules

TL;DR

This study uses lattice QCD to compute light-by-light scattering amplitudes and compares them with dispersive sum rule models, providing crucial insights for estimating the muon's anomalous magnetic moment.

Contribution

It presents the first lattice QCD calculation of the eight forward light-by-light scattering amplitudes and compares them with dispersive sum rule models, including disconnected diagrams.

Findings

Lattice results agree with large-N inspired predictions for disconnected diagrams.

Provides monopole and dipole mass parameters for resonance transition form factors.

Offers data to improve phenomenological estimates of muon g-2 contributions.

Abstract

The hadronic contribution to the eight forward amplitudes of light-by-light scattering ($\gamma^*\gamma^*\to \gamma^*\gamma^*$) is computed in lattice QCD. Via dispersive sum rules, the amplitudes are compared to a model of the $\gamma^*\gamma^*\to {\rm hadrons}$ cross sections in which the fusion process is described by hadronic resonances. Our results thus provide an important test for the model estimates of hadronic light-by-light scattering in the anomalous magnetic moment of the muon, $a_\mu^{\rm HLbL}$. Using simple parametrizations of the resonance $M\to \gamma^*\gamma^*$ transition form factors, we determine the corresponding monopole and dipole masses by performing a global fit to all eight amplitudes. Together with a previous dedicated calculation of the $\pi^0\to \gamma^*\gamma^*$ transition form factor, our calculation provides valuable information for phenomenological estimates of $a_\mu^{\rm HLbL}$. The presented calculations are performed in two-flavor QCD with pion masses extending down to 190\,MeV at two different lattice spacings. In addition to the fully connected Wick contractions, on two lattice ensembles we also compute the (2+2) disconnected class of diagrams, and find that their overall size is compatible with a parameter-free, large-$N$ inspired prediction, where $N$ is the number of colors. Motivated by this observation, we estimate in the same way the disconnected contribution to $a_\mu^{\rm HLbL}$.