The isospin-violating part of the hadronic vacuum polarisation

Abstract

We present our calculation of the isospin-violating part of the hadronic vacuum polarisation (HVP) contribution to muon $(g-2)$ in lattice QCD at the $SU(3{)}_{\mathrm{f}}$ symmetric point. The computation of the contributing fully connected diagrams with one internal photon as well as the computation of the only (mass) counterterm are shown. The latter is determined from the charged-neutral kaon mass splitting. We employ coordinate-space methods and a photon propagator which is regulated à la Pauli-Villars with a cutoff scale $\Lambda$ well below the lattice cutoff. This regularization makes it possible for us to do crosschecks of individual contributions with calculations in the continuum. Our continuum extrapolated results show little to no dependence on $\Lambda$. This makes our final limit $\Lambda \to \infty$ straightforward.