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Recently, the Budapest-Marseille-Wuppertal collaboration achieved sub-percentprecision in the evaluation of the lowest-order hadronic vacuum polarizationcontribution to the muon $g_\mu-2$ (arXiv:hep-lat/2002.12347v3). At this levelof precision, isospin-symmetric QCD is not sufficient. In this contribution wereview how QED and strong-isospin-breaking effects have been included in ourwork. Isospin breaking is implemented by expanding the relevant correlationfunctions to second order in the electric charge $e$ and to first order in$m_u-m_d$. The correction terms are then computed using isospin-symmetricconfigurations. The choice of this approach allows us to better distribute theavailable computing resources among the various contributions.

QED and strong isospin corrections in the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon