Pion and Kaon box contribution to aμHLbL

Abstract

We present an evaluation of the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${K}^{\ifmmode\pm\else\textpm\fi{}}$ box contributions to the hadronic light-by-light piece of the muon's anomalous magnetic moment, ${a}_{\ensuremath{\mu}}$. The calculation of the corresponding electromagnetic form factors (EFFs) is performed within a Dyson-Schwinger equations (DSE) approach to quantum chromodynamics. These form factors are calculated in the so-called rainbow-ladder (RL) truncation, following two different evaluation methods and, subsequently, in a further improved approximation scheme which incorporates meson cloud effects. The results are mutually consistent, indicating that in the domain of relevance for ${a}_{\ensuremath{\mu}}$ the obtained EFFs are practically equivalent. Our analysis yields the combined estimates of ${a}_{\ensuremath{\mu}}^{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}\mathrm{box}}=\ensuremath{-}(15.6\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and ${a}_{\ensuremath{\mu}}^{{K}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{-}\mathrm{box}}=\ensuremath{-}(0.48\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$, in full agreement with results previously obtained within the DSE formalism and other contemporary estimates.