Single pseudoscalar meson pole and pion box contributions to the anomalous magnetic moment of the muon

We present results for single pseudoscalar meson pole contributions and pion box contributions to the hadronic light-by-light (LBL) correction of the muon’s anomalous magnetic moment. We follow the recently developed dispersive approach to LBL, where these contributions are evaluated with intermediate mesons on-shell. However, the space-like electromagnetic and transition form factors are not determined from analytic continuation of time-like data, but directly calculated within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. This strategy allows for a systematic comparison with a strictly dispersive treatment and also with recent results from lattice QCD. Within error bars, we obtain excellent agreement for the pion electromagnetic and transition form factor and the resulting contributions to LBL. In addition, we present results for the $\eta$ and ${\eta }^{\mathrm{\prime }}$ pole contributions and discuss the dynamical effects in the $\eta -{\eta }^{\mathrm{\prime }}$ mixing due to the strange quarks. Our result for the total pseudoscalar pole contributions is $a_\mu^{$\text{PS-pole}$} = 91.6 ,(1.9) \times 10^{-11}$andforthepion-boxcontributionweobtain$a_\mu^{\pi-$\text{box}$} = -16.3 ,(2)(4) \times 10^{-11}$.