In the anomalous magnetic moment of the muon, the determination of the hadronic vacuum polarization (HVP) contribution must reach sub-percent precision in order for the Standard Model prediction to match the precision of the experimental measurement. To achieve this, one needs to include QED corrections that break isospin symmetry, which is usually imposed in lattice calculations. A common approach is to treat these corrections perturbatively in the electromagnetic fine-structure constant, expressing them through Feynman diagrams with hadronic n-point functions calculated in isospin symmetric QCD, where individual vertices are connected by the photon propagator.

We present a lattice QCD calculation of one of the disconnected diagrams, which is UV-finite and not suppressed by SU(3) flavour symmetry. The calculation is performed on 14 ensembles using a coordinate-space framework and the photon propagator in the continuum and infinite volume. Additionally, we investigate a phenomenological model including the effects of the charged and neutral pion, as well as the $\eta$- and $\eta'$-meson. The model is used to approximate the tail of the integrand computed on the lattice and as an ansatz for the pion mass dependence of the result.