We have calculated the step scaling function and the running coupling of QCD in the Schrödinger functional scheme with four flavors of O(a) improved Wilson quarks. Comparisons of our non-perturbative results with 2-loop and 3-loop perturbation theory as well as with non-perturbative data for only two flavors are made.

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We discuss the status of different determinations of α 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 µ. Such results already exist in the SF-scheme for N f = 0, 2 [1,2] and N f = 3 [3]. We recently added the running with four massless flavours in a range of α from about 0.07 to 0.3 . It is based on our recent determination of the Sheikholeslami Wohlert coefficient in the four-flavour theory.

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