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Regular Article - Theoretical Physics

Hadronic light-by-light contribution to (g − 2)µ from lattice QCD with SU(3) flavor symmetry En-Hung Chao1, Antoine Gérardin2 , Jeremy R. Green3 , Renwick J. Hudspith1, Harvey B. Meyer1,4,a 1

PRISMA+ Cluster of Excellence and Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany 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

2

Received: 17 July 2020 / Accepted: 6 September 2020 © The Author(s) 2020

Abstract We perform a lattice QCD calculation of the hadronic light-by-light contribution to (g − 2)μ at the SU(3) flavor-symmetric point m π = m K  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 aμhlbl = (65.4±4.9±6.6)×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.

1 Introduction Electrons and muons carry a magnetic moment aligned with their spin. The proportionality factor between the two axial vectors is parameterized by the gyromagnetic ratio g. In Dirac’s theory, g = 2, and for a lepton family  one chara e-mail:

[email protected] (corresponding author)

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acterizes the deviation of g from this reference value by a = (g − 2) /2. Historically, the ability of quantum electrodynamics (QED) to quantitatively predict this observable played a crucial role in establishing quantum field theory as the framework in which particle physics theories are formulated. Presently, the achieved experimental precision on the measurement of the anomalous magnetic moment of the muon [1], aμ , is 540 ppb. At this level of precision, such a measurement tests not only QED, but also the effects of the weak and the strong interaction of the Standard Model (SM) of particle physics. Currently