Kaon-box contribution to the anomalous magnetic moment of the muon
Gernot Eichmann, Christian S. Fischer, Richard Williams
Abstract
We present results for the charged kaon-box contributions to the hadronic light-by-light (HLBL) correction of the muon's anomalous magnetic moment. To this end we determine the kaon electromagnetic form factor within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations and evaluate the kaon-box contribution as defined in the dispersive approach to HLBL. As an update to previous work we also reevaluate the charged pion-box contribution taking effects due to isospin breaking into account. Our results are ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}\mathrm{box}}=\ensuremath{-}15.7(2)(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and ${a}_{\ensuremath{\mu}}^{{K}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}\mathrm{box}}=\ensuremath{-}0.48(2)(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ thus confirming the large suppression of box contributions beyond the leading pion box.