Pion and Kaon box contribution to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mi>HLbL</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math>

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