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.

arXiv commentUpdated error estimates. 10 pages, 2 figures, 2 tables

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