https://doi.org/10.1140/epjc/s10052-020-08444-3
Regular Article – Theoretical Physics
Hadronic light-by-light contribution to 
from lattice QCD with SU(3) flavor symmetry
1
PRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany
2
Aix-Marseille University, Université de Toulon, CNRS, CPT, Marseille, France
3
Theoretical Physics Department, CERN, 1211, Geneva 23, Switzerland
4
Helmholtz Institut Mainz, Johannes Gutenberg-Universität Mainz, 55099, Mainz, Germany
Received:
17
July
2020
Accepted:
6
September
2020
Published online:
20
September
2020
We perform a lattice QCD calculation of the hadronic light-by-light contribution to at the SU(3) flavor-symmetric point 
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 
, 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.
© The Author(s) 2020
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