## Electromagnetic corrections to the hadronic vacuum polarization of the photon within QED_L and QED_M

Preprint number: CP3-Origins-2017-41 DNRF90
Authors: Andrea Bussone (CP3-Origins & DIAS), Tadeuz Janowski (CP3-Origins & DIAS), and Michele Della Morte (CP3-Origins & DIAS)
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. In addition we make sure that the volumes and photon masses used in QED$$_{\rm M}$$ are such that the correct dispersion relation is reproduced by the energy levels extracted from the charged pions two-point functions. Finally we compare results for pion masses and the HVP between QED$$_{\rm L}$$ and QED$$_{\rm M}$$. For the vacuum polarization, corrections with respect to the pure QCD case, at fixed pion masses, turn out to be at the percent level.