Running of the SF-coupling with four massless flavours

We discuss the status of different determinations of alpha_s, motivating a precise and reliable computation from lattice QCD. In order to suppress perturbative errors, the non-perturbative computation has to reach high energy scales mu. Such results already exist in the SF-scheme for N_f=0,2 and N_f=3. We recently added the running with four massless flavours in a range of alpha from about 0.07 to 0.3 . It is based on our recent determination of the Sheikholeslami Wohlert coefficient in the four-flavour theory.
Comment: 7 pages, Lattice 2010 proceedings