We investigate the possibility of using numerical stochastic perturbation theory (NSPT) to probe high orders in the perturbative expansion of lattice gauge theories with massless Wilson fermions. Twisted boundary conditions are used to regularise the gauge zero-mode; the extension of these boundary conditions to include fermions in the fundamental representation requires to introduce a smell degree of freedom. Moreover, the mass of Wilson fermions is affected by an additive renormalisation: we study how to determine the mass counterterms consistently at finite volume. The knowledge of the critical masses will enable high-order perturbative computations in massless QCD, e.g. (as a first application) for the plaquette.

Theoretical Developments