Pion and Kaon box contribution to aμHLbL

Abstract

We present an evaluation of the π ± and K ± box contributions to the hadronic light-by-light piece of the muon’s anomalous magnetic moment, a μ . 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 μ the obtained EFFs are practically equivalent. Our analysis yields the combined estimates of a π ± − box μ = − ( 15.6 ± 0.2 ) × 10 − 11 and a K ± − box μ = − ( 0.48 ± 0.02 ) × 10 − 11 , in full agreement with results previously obtained within the DSE formalism and other contemporary estimates.