Hadronic light-by-light contribution to $(g-2)_\mu$ from lattice QCD with SU(3) flavor symmetry

TL;DR

This paper presents a lattice QCD calculation of the hadronic light-by-light contribution to the muon's anomalous magnetic moment at an SU(3) flavor-symmetric point, employing coordinate-space perturbation theory and novel computational techniques.

Contribution

It introduces a new lattice QCD approach with continuum QED elements, a sparse-grid method for disconnected diagrams, and extends previous work to estimate the physical quark mass limit.

Findings

Calculated $a_\mu^{\rm hlbl}$ as $(65.4\pm 4.9 \pm 6.6)\times 10^{-11}$

Demonstrated equivalence of two methods for connected contributions

Extended the tail of the integrand using previous pion form factor data

Abstract

We perform a lattice QCD calculation of the hadronic light-by-light contribution to $(g-2)_\mu$ at the SU(3) flavor-symmetric point $m_\pi=m_K\simeq 420\,$MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtain $a_\mu^{\rm hlbl} = (65.4\pm 4.9 \pm 6.6)\times 10^{-11}$, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.