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We discuss leading isospin breaking effects in the hadronic vacuum polarisation required for the investigation of the hadronic contribution to $(g-2)_{\mu}$. The calculation proceeds by expanding the relevant correlation functions around the isosymmetric limit. Isosymmetric observables are evaluated on gauge ensembles with $N_{f}=2+1$, $O(a)$ improved Wilson fermions and open boundary conditions generated by the CLS effort. Particular emphasis is placed on the relevant quark-disconnected diagrams required for a complete treatment of leading isospin breaking effects in the valence quark sector. We provide a detailed discussion of the renormalisation of the vector current in QCD+QED taking operator mixing into account.

Leading isospin breaking effects in the hadronic vacuum polarisation with open boundaries