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We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schrödinger functional scheme. The corresponding Λ-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic "experimentally" observable quantity. We find the non-perturbative evolution of the coupling important to eliminate a significant contribution to the total error in the estimated Λ-parameter.

The scaling of the Schrödinger functional coupling is studied numerically and perturbatively for an SU(3) lattice gauge field coupled to an O(a) improved bosonic spinor field. This corresponds to QCD with minus two light flavours and is used as a numerically less costly test case for real QCD. A suitable algorithm is developed, and the influence of the matter fields on the continuum limit and the lattice artefacts are studied in detail.

As a prerequisite to dynamical fermion simulations a detailed study of optimal parameters and scaling behavior is conducted for the quenched Schr\"odinger functional at fixed renormalized coupling. We compare standard hybrid overrelaxation techniques with local and global hybrid Monte Carlo. Our efficiency measure is designed to be directly relevant for the strong coupling constant as used by the ALPHA collaboration.Comment: LATTICE99 - 6 pages, 6 figures; added referenc

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