Hadronic light-by-light scattering amplitudes from lattice QCD versus dispersive sum rules

2017/12/01 by Antoine Gérardin, Jeremy Green, Oleksii Gryniuk +4
Physics and Astronomy · #Amplitude #Anomalous magnetic dipole moment #Dipole #Hadron #High-Energy Particle Collisions Research #Isospin #Lattice (music) #Lattice QCD #Lattice field theory #Muon #Particle physics #Particle physics theoretical and experimental studies #Physics #Pion #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Scattering #Scattering amplitude #Sum rule in quantum mechanics #hep-lat #hep-ph

paper · pdf · doi:10.1103/physrevd.98.074501

published as Phys. Rev. D 98, 074501 (2018) · 41 pages, 10 figures with up to 8 panels

arxiv created 2017/12/01 · openalex created_date 2017/12/22 · openalex publication_date 2018/10/02 · arxiv updated 2018/10/10 · openalex updated_date 2026/08/05

Abstract

The hadronic contribution to the eight forward amplitudes of light-by-light scattering (\ensuremathγ^*\ensuremathγ^*\ensuremath→\ensuremathγ^*\ensuremathγ^*) is computed in lattice QCD. Via dispersive sum rules, the amplitudes are compared to a model of the \ensuremathγ^*\ensuremathγ^*\ensuremath→hadrons cross sections in which the fusion process is described by hadronic resonances. Our framework can provide an important test for the model estimates of hadronic light-by-light scattering in the anomalous magnetic moment of the muon, a_\ensuremathμ^HLbL. Using simple parametrizations of the resonance M\ensuremath→\ensuremathγ^*\ensuremathγ^* transition form factors, we determine the corresponding monopole and dipole masses by performing a global fit to all eight amplitudes. Together with a previous dedicated calculation of the \ensuremathπ⁰\ensuremath→\ensuremathγ^*\ensuremathγ^* transition form factor, our calculation provides valuable information for phenomenological estimates of a_\ensuremathμ^HLbL. The presented calculations are performed in two-flavor QCD with pion masses extending down to 190 MeV at two different lattice spacings. In addition to the fully connected Wick contractions, on two lattice ensembles we also compute the (2+2) disconnected class of diagrams, and find that their overall size is compatible with a parameter-free, large-N inspired prediction, where N is the number of colors. Motivated by this observation, we estimate in the same way the disconnected contribution to a_\ensuremathμ^HLbL.

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