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

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 $a_{\mu }^{\mathrm{hlbl}}=(65.4\pm 4.9\pm 6.6)\times 10^{-11}$, 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.

19 figures, 39 pages; improved references, in particular concerning the eta exchange; no figures or results changed

References in corpus (8)

• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass
• Electromagnetic and spin polarisabilities in lattice QCD
• Quark disconnected diagrams in chiral perturbation theory
• Pion light-by-light contributions to the muon $g-2$

Cited by in corpus (16)

• 50 Years of Quantum Chromodynamics
• Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$ from lattice QCD: a complete calculation
• The charm-quark contribution to light-by-light scattering in the muon $(g-2)$ from lattice QCD
• The anomalous magnetic moment of the muon: status of Lattice QCD calculations
• NNLO virtual and real leptonic corrections to muon-electron scattering
• Improved ${\pi }^0,\eta ,{\eta }^{\prime }$ transition form factors in resonance chiral theory and their $a_{\mu }^{\mathrm{HLbL}}$ contribution
• Forward light-by-light scattering and electromagnetic correction to hadronic vacuum polarization
• $\tau$ data-driven evaluation of Euclidean windows for the hadronic vacuum polarization
• Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel
• Coordinate-space calculation of the window observable for the hadronic vacuum polarization contribution to $(g-2{)}_{\mu }$
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$
• Theory of Muon g-2