_{μ}since they involve the lattice calculation of the hadronic vacuum polarisation. In the case of the electromagnetic coupling α, its low-energy value is known to a precision of 0.3 ppb, but the value of α(m

_{Z}

^{2}) is known only to 0.1 ‰, and a larger portion of the difference in uncertainty is due to the hadronic contribution to the running of α, i.e. the hadronic vacuum polarization. Phenomenologically this can be estimated through the R-ratio, but this results in relatively large errors at low Q

^{2}. On the lattice, the hadronic vacuum polarization can be measured through the correlator of vector currents, and currently a determination of the running of α in agreement with phenomenology and with similar errors can be achieved, so that in the future lattice results are likely to take the lead here. In the case of the electroweak mixing angle, sin

^{2}θ

_{w}is known well at the Z pole, but only poorly at low energy, although a number of experiments (including the P2 experiment at Mainz) are aiming to reduce the uncertainty at lower energies. Again, the running can be determined from the Z-γ mixing through the associated current-current correlator, and current efforts are under way, including an estimation of the systematic error caused by the omission of quark-disconnected diagrams.

The second speaker was Vittorio Lubicz, who looked at the opposite problem, i.e. the electroweak corrections to hadronic observables. Since approximately α=1/137, electromagnetic corrections at the one-loop level will become important once the 1% level of precision is being aimed for, and since the up and down quarks have different electrical charges, this is an isospin-breaking effect which also necessitates at the same time considering the strong isospin breaking caused by the difference in the up and down quark masses. There are two main methods to include QED effects into lattice simulations; the first is direct simulations of QCD+QED, and the second is the method of incorporating isospin-breaking effects in a systematic expansion pioneered by Vittorio and colleagues in Rome. Either method requires a systematic treatment of the IR divergences arising from the lack of a mass gap in QED. In the Rome approach this is done through splitting the Bloch-Nordsieck treatment of IR divergences and soft bremsstrahlung into two pieces, whose large-volume limits can be taken separately. There are many other technical issues to be dealt with, but first physical results from this method should be forthcoming soon.

In the afternoon there was a discussion about QED effects and the range of approaches used to treat them.