  We study the lattice artefacts of the Wilson Dirac operator for QCD with two
colors and fermions in the fundamental representation from the viewpoint of
chiral perturbation theory. These effects are studied with the help of the
following spectral observables: the level density of the Hermitian Wilson Dirac
operator, the distribution of chirality over the real eigenvalues, and the
chiral condensate for the quenched as well as for the unquenched theory. We
provide analytical expressions for all these quantities. Moreover we derive
constraints for the level density of the real eigenvalues of the non-Hermitian
Wilson Dirac operator and the number of additional real modes. The latter is a
good measure for the strength of lattice artefacts. All computations are
confirmed by Monte Carlo simulations of the corresponding random matrix theory
which agrees with chiral perturbation theory of two color QCD with Wilson
fermions.
