Kaon-box contribution to the anomalous magnetic moment of the muon

Abstract

We present results for the charged kaon-box contributions to the hadronic light-by-light (HLBL) correction of the muon's anomalous magnetic moment. To this end we determine the kaon electromagnetic form factor within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations and evaluate the kaon-box contribution as defined in the dispersive approach to HLBL. As an update to previous work we also re-evaluate the charged pion-box contribution taking effects due to isospin breaking into account. Our results are $a_{\mu }^{{\pi }^{\pm }-\text{box}}=-15.7(2)(3)\times 10^{-11}$ and $a_{\mu }^{K^{\pm }-\text{box}}=-0.48(2)(4)\times 10^{-11}$ thus confirming the large suppression of box contributions beyond the leading pion box.

Comments: 6 pages, 4 figures; v3: improved numerics, updated number for kaon-box, conclusions unchanged. arXiv admin note: text overlap with arXiv:1903.10844