I provide updates for the theoretical predictions of the muon and electron anomalous magnetic moments, for the shift in the fine structure constant α(MZ )and for the weak mixing parameter $ \mathop {\sin }\nolimits^2 \mathop \Theta \nolimits_w (\mathop M\nolimits_Z ) $. Phenomenological results for Euclidean time correlators, the key objects in the lattice QCD approach to hadronic vacuum polarization, are briefly considered. Furthermore,I present a list of isospin breaking and electromagnetic corrections for the lepton moments, which may be used to supplement lattice QCD results obtained in the isospin limit and without the e.m. corrections.
On isospin breaking in $\tau$ decays for $(g-2)_\mu$ from Lattice QCD