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.
Highlights
With a persistent discrepancy of about 3–4 standard deviations between the theoretical Standard Model (SM)predictions and experimental determinations [1], the anomalous magnetic moment aμ 1⁄4 1 2 ðg −the muon is a highly interesting quantity
We present results for the charged kaon-box contributions to the hadronic light-by-light (HLBL) correction of the muon’s anomalous magnetic moment
While we described the various steps needed to calculate the electromagnetic form factor of the pion in Ref. [29], here we detail the changes that arise for the kaon electromagnetic form factor (EMFF) in the functional DSE approach
Summary
With a persistent discrepancy of about 3–4 standard deviations between the theoretical Standard Model (SM). In the theoretical SM calculations the error budget is dominated by QCD corrections, i.e., hadronic vacuum polarization and hadronic light-by-light (HLBL) scattering effects. In contrast to a purely data-driven dispersive framework, the necessary pseudoscalar transition form factors have not been extracted from experiment but calculated using DSEs and BSEs. The central values of the pseudoscalar pole contributions to aμ obtained in Ref. The pion-box contribution to HLBL has been determined in the functional approach [29] using the pion electromagnetic form factor calculated from the underlying. We use a Euclidean notation throughout this work; see e.g., Appendix A of Ref. [34] for conventions
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