A determination of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon from lattice QCD aiming at a precision of 1% requires to include isospin breaking corrections in the computation. We present a lattice calculation of the QED and strong isospin breaking corrections to the hadronic vacuum polarization with Domain Wall fermions. The results are obtained using quark masses which are tuned such that pion and kaon masses agree with their physical values including isospin breaking corrections.

The hadronic vacuum polarization can be determined from the vector correlator in a mixed timemomentum representation. We explicitly calculate the disconnected contribution to the vector correlator, both in the N f = 2 theory and with an additional quenched strange quark, using non-perturbatively O(a)-improved Wilson fermions. All-to-all propagators are computed using stochastic sources and a generalized hopping parameter expansion. Combining the result with the dominant connected contribution, we are able to estimate an upper bound for the systematic error that arises from neglecting the disconnected contribution in the determination of (g − 2) µ .

We study the leading hadronic contribution to γ-Z mixing, which determines the leading order hadronic contribution to the running of the electroweak mixing angle θ W . The required vacuum polarization function Π γZ is calculated from the appropriate vector correlation functions in a mixed time-momentum representation. We explicitly calculate the connected and the disconnected contributions to such vector correlators using N f = 2 dynamical flavors of nonperturbatively O(a)-improved Wilson fermions.

The decays and mixing of K mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant G F and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of lattice QCD make high-precision standard model predictions possible. Here we discuss and attempt to forecast some of these capabilities.

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