Hadronic light-by-light contribution to $(g-2)_\mu$ from lattice QCD: a complete calculation

TL;DR

This paper presents a comprehensive lattice QCD calculation of the hadronic light-by-light scattering contribution to the muon g-2, providing a precise estimate that confirms this contribution cannot account for the existing discrepancy between theory and experiment.

Contribution

It offers the first complete lattice QCD calculation of the hadronic light-by-light contribution including all Wick contractions and multiple simulation parameters.

Findings

The calculated contribution is $106.8(14.7) imes 10^{-11}$.

Results are consistent with phenomenological estimates and previous lattice studies.

The contribution cannot explain the current muon g-2 discrepancy.

Abstract

We compute the hadronic light-by-light scattering contribution to the muon $g-2$ from the up, down, and strange-quark sector directly using lattice QCD. Our calculation features evaluations of all possible Wick-contractions of the relevant hadronic four-point function and incorporates several different pion masses, volumes, and lattice-spacings. We obtain a value of $a_\mu^{\text{Hlbl}} = 106.8(14.7) \times 10^{-11}$ (adding statistical and systematic errors in quadrature), which is consistent with current phenomenological estimates and a previous lattice determination. It now appears conclusive that the hadronic light-by-light contribution cannot explain the current tension between theory and experiment for the muon $g-2$.