Electromagnetic corrections to the hadronic vacuum polarization of the photon within QED$_{\rm L}$ and QED$_{\rm M}$

Understand

We compute the leading QED corrections to the hadronic vacuum polarization (HVP) of the photon, relevant for the determination of leptonic anomalous magnetic moments, $a_\ell$.

• We work in the electroquenched approximation and use dynamical QCD configurations generated by the CLS initiative with two degenerate flavors of non-perturbatively O($a$)-improved Wilson fermions.
• We consider QED$_{\rm L}$ and QED$_{\rm M}$ to deal with the finite-volume zero modes.
• We compare results for the Wilson loops with exact analytical determinations.