Pion and Kaon box contribution to $a_{\mu}^{\text{HLbL}}$

Abstract

We present an evaluation of the $\pi^\pm$ and $K^\pm$ box contributions to the hadronic light-by-light piece of the muon's anomalous magnetic moment, $a_\mu$. 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 $a_\mu$ the obtained EFFs are practically equivalent. Our analysis yields the combined estimates of $a_\mu^{\pi^\pm-box}=-(15.6\pm 0.2)\times 10^{-11}$ and $a_\mu^{K^\pm-\text{box}}=-(0.48\pm 0.02)\times 10^{-11}$, in full agreement with results previously obtained within the DSE formalism and other contemporary estimates.