The step scaling function of QCD at negative flavor number
  As a computationally less costly test case for full QCD, we investigate an SU(3) Yang-Mills theory coupled to a bosonic spinor field. This theory corresponds to QCD with minus two quark flavors and is known as the bermion model. Our central object of interest is the step scaling function which describes the scale evolution of the running coupling in the Schrodinger functional scheme. We develop a suitable algorithm for the simulation of O(a) improved bermions and compare its performance with unimproved bermions and full QCD. We study in detail the lattice artefacts and the continuum extrapolation of the step scaling function from lattice simulations when improvement is used. Our results are compared to the unimproved bermion and dynamical fermion cases, and to renormalized perturbation theory in the continuum limit.   We also examine the step scaling function with massive quarks in the bermion model. According to the Appelquist-Carazzone theorem the contributions from matter fields are expected to vanish for large masses, such that the step scaling function converges to the pure gauge theory case. If one wants to connect non-perturbatively different effective theories with different numbers of active quarks over flavor thresholds, lattice artefacts should be reasonably small. In order to test the feasibility of such a method, we investigate the step scaling function and its lattice artefacts for several values of the mass. 
Bernd Gehrmann