Pion and Kaon box contribution to aμHLbL

The authors acknowledge support from CONACYT and Cátedras Marcos Moshinsky (Fundación Marcos Moshinsky). This research was also supported by CONACYT grant ‘Paradigmas y Controversias de la Ciencia 2022’ (Project No. 319395) and by Coordinación de la Investigación Científica (CIC) of the University of Michoacán, M´exico, through Grant No. 4.10.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.CONACYT and Cátedras Marcos Moshinsky (Fundación Marcos Moshinsky)CONACYT (Project No. 319395)Coordinación de la Investigación Científica Grant No. 4.10